%WachiKuniiMiyoshi1999
\rhl{W}
\refR Wachi, T., Kunii, T. L., Miyoshi, K.;
Architecture of a generation rule-oriented D-surface database 
system SURFDATA and its application to interactive apparel 
design; xxx; 1999;

%Wachspress1975
% . 20nov03
\rhl{}
\refB Wachspress, Eugene;
A Rational Finite Element Basis;
Academic Press (xxx); 1975;

%Wagner1986
% larry
\rhl{W}
\refD Wagner, M.;
Strikte Approximationen und stetige Selektionen der metrischen 
Projektion in schwach tschebyscheffschen R\"aumen;
Univ.\ Erlangen; 1986;

%WagnerPottmann1994
% larry
\rhl{W}
\refP Wagner, M. G., Pottmann, H.;
Symmetric tb--spline schemes;
\ChamonixIIa; 483--490;

%Wahba1971
% larry
\rhl{W}
\refJ Wahba, G.;
On the regression design problem of Sacks and Ylvisaker;
Annals Math.\ Stat.; 42; 1971; 1035--1053;

%Wahba1972
\rhl{W}
\refR Wahba, G.;
More on regression design, with applications;
Univ.\ Wisconsin; 1972;

%Wahba1973a
\rhl{W}
\refR Wahba, G.;
Convergence properties of the method of regularization for 
noisy linear operator equations;
MRC \#1132; 1973;

%Wahba1973b
% larry
\rhl{W}
\refJ Wahba, G.;
On the minimization of a quadratic functional subject to a 
continuous family of linear inequality constraints;
SIAM J.\ Control; 11; 1973; 64--79;

%Wahba1973c
% carl
\rhl{W}
\refJ Wahba, Grace;
Convergence rates of certain approximate solutions of Fredholm integral
   equations of the first kind;
\JAT; 7(2); 1973; 167--185;

%Wahba1975
% carl
\rhl{W}
\refJ Wahba, Grace;
Smoothing noisy data with spline functions;
\NM; 24; 1975; 383--393;

%Wahba1975b
\rhl{W}
\refJ Wahba,  G.;
Interpolating spline methods for density
	 estimation.\  Equi-spaced knots;
Ann.\  Statist.; 3; 1975;  30--48;

%Wahba1975c
\rhl{W}
\refR Wahba,  G.;
A canonical form for the problem of estimating smooth surfaces;
Rpt.\ 420, Univ.\ Wisc.\ Stat.; 1975;

%Wahba1978b
\rhl{W}
\refJ Wahba,  G.;
Improper priors, spline smoothing, and the problem of
guarding against model errors in regression;
J. Royal Stat.\ Soc.\ B; 40; 1978; 364--372;

%Wahba1978c
\rhl{W}
\refR Wahba,  G.;
Interpolating surfaces:  high order convergence rates
and their associated designs, with application
to X-ray image reconstruction;
Rpt.\ 523, Univ.\ Wisc.\ Stat.; 1978;

%Wahba1979a
\rhl{W}
\refQ Wahba,  G.;
Practical techniques of optimal smoothing, with application to the
numerical differentiation of noisy data and smoothing of log spectral
density estimates;
(Classification and Clustering),
J. Van Ryzin (ed.), Academic Press (New York); 1979; 423--458;

%Wahba1979b
\rhl{W}
\refQ Wahba,  G.;
Convergence rate of thin plate smoothing splines when the data are noisy;
(Smoothing Techniques for Curve Estimation),
T. G. M. Rosenblatt (ed.), Springer Verlag (Berlin); 1979; 232--246;

%Wahba1979c
\rhl{W}
\refQ Wahba,  G.;
Smoothing and ill--posed problems;
(Solution Methods for Integral Equations with Applications),
M. Goldberg (ed.), Plenum (New York); 1979; 183--194;

%Wahba1979d
\rhl{W}
\refQ Wahba,  G.;
How to smooth curves and surfaces with splines and
cross-validation;
(Proceedings 24th Conference on Design of Experiments), xxx (ed.),
U. S. Army  Research Office (Triangle Research Park NC); 1979; 167--192;

%Wahba1980
% larry
\rhl{W}
\refP Wahba,  G.;
Spline bases, regularization, and generalized cross
validation for solving approximation problems with large
quantities of noisy data;
\TexasIII; 905--912;

%Wahba1981
\rhl{W}
\refJ Wahba,  G.;
Numerical experiments with the thin plate histospline;
Com.\ Stat.\ Theor.\ Math.; A10; 1981; 2475--2514;

%Wahba1981b
\rhl{W}
\refJ Wahba,  G;
Spline interpolation and smoothing on the sphere;
\SJSSC; 2; 1981; 5--16;

%Wahba1981c
\rhl{W}
\refJ Wahba,  G.;
 Data-based optimal smoothing of orthogonal series density estimates;
Ann.\ Stat.; 9; 1981; 146--156;

%Wahba1982
\rhl{W}
\refJ Wahba,  G.;
Errata: Spline interpolation and smoothing on the sphere;
\SJSSC; 3; 1982; 385--386;

%Wahba1982b
\rhl{W}
\refP Wahba,  G.;
Vector splines on the sphere, with application to
the estimation of vorticity and divergence from discrete, noisy data;
\MvatII;  407--429;

%Wahba1982c
% sherm, pulisher update
\rhl{W}
\refQ Wahba,  G.;
Constrained regularization for ill posed linear
operator equations, with applications in meteorology and medicine;
(Statistical Decision Theory and Related Topics III, Vol.2),
S. S. Gupta and J. O. Berger (eds.), Academic Press (New York); 1982; 383--418;

%Wahba1982d
\rhl{W}
\refQ Wahba,  G.;
Variational methods in simultaneous optimum
interpolation and initialization;
(The Interaction Between Objective Analysis and Initialization),
D. Williamson (ed.), NCAR Publication in Meterology 127 (Boulder CO); 1982; XX;

%Wahba1983
% . 20apr00
\rhl{W}
\refJ Wahba,  G.;
Bayesian ``confidence intervals'' for the cross-validated smoothing spline;
J. Roy.\ Statist.\ Soc.\ Ser.\ B; 45; 1983; 133--150;
% includes discussion of GCV estimates for smoothing parameter that are quite
% wrong

%Wahba1984a
\rhl{W}
\refQ Wahba,  G.;
Cross validated spline methods for the estimation of multivariate
functions from data on functionals;
(Statistics, an Appraisal),
H. A. David and H. T. Davis (eds.),
Iowa State University Press (xxx); 1984; 205--235;

%Wahba1984b
\rhl{W}
\refJ Wahba,  G.;
Surface fitting with scattered noisy data on Euclidean $d-$\break space and on
the sphere;
\RMJM; 14; 1984; 281--299;

%Wahba1984c
% .
\rhl{W}
\refQ Wahba,  G.;
Partial spline models for the semiparametric estimation of functions of several
variables;
(Analyses for Time Series, Japan-U.S.\ Joint Seminar), xxx (ed.), Institute of
Statistical Mathematics (Tokyo); 1984; xxx--xxx;

%Wahba1985a
% larry
\rhl{W}
\refQ Wahba,  G.;
Variational methods for multidimensional inverse problems;
(Remote Sensing Retrieval Methods),
A. Deepak, H. Fleming, and M. Chahine (eds.), 
A. Deepak Publ.\ (xxx); 1985; 385--407;

%Wahba1985b
% sherm, publisher update
\rhl{W}
\refQ Wahba,  G.;
Multivariate thin plate spline smoothing with positivity and other linear
inequality constraints;
(Statistical Image Processing and Graphics),
E. Wegman and E. J. dePriest (eds.), Marcel Dekker (New York); 1985; 275--290;

%Wahba1985c
% larry
\rhl{W}
\refJ Wahba,  G.;
A comparison of GCV and GML for choosing the smoothing parameter in the 
generalized spline smoothing problem;
The Annals of Statistics; 13; 1985; 1378--1402;

%Wahba1986a
% larry
\rhl{W}
\refQ Wahba,  G.;
Partial and interaction splines for the semiparametric estimation of
functions of several variables;
(Computer Science and Statistics, Proceedings of the 18th Symposium on the 
Interface), T. J.  Boardman (ed.), Amer.\ Stat.\ Assoc.\ (Washington); 1986; 75--80;

%Wahba1986b
% sherm, editor update
\rhl{W}
\refQ Wahba,  G.;
Partial spline modelling of the tropopause and other discontinuities;
(Function Estimates),  J. S. Marron (ed.),
Contemporary Mathematics Vol.\ 59, Amer.\ Math.\  Soc.\ (Providence);
1986; 125--135;

%Wahba1986c
% sherm, publisher update
\rhl{W}
\refQ Wahba,  G.;
Partial spline models for the estimation of three dimensional atmospheric
temperature distribution from satellite radiance data and tropopause
height information;
(Variational Methods in Geosciences), Y. K. Sasaki (ed.),
Elsevier (New York); 1986; 125--150;

%Wahba1990a
% .
\rhl{W}
\refB Wahba,  G.;
Spline Models for Observational Data;
CBMS-NSF Regional Conference Series in Applied Mathematics 59, SIAM
(Philadelphia, PA); 1990;

%Wahba1999
\rhl{W}
\refJ Wahba, G.;
Convergence rates for certain approximate solutions to Fredholm 
integral equations of the first kind;
\JAT; xx; 1999; xx--xx;

%WahbaVillalobos1983
\rhl{W}
\refJ Wahba,  G., Villalobos, M. A.;
Multivariate thin plate spline estimates for the posterior probabilities
in the classification problem;
Comm.\ Statist.\ Theor.\ Meth.; 12; 1983; 1449--1479;

%WahbaWangY1987
\rhl{W}
\refR Wahba, G., Wang, Y.;
When is the optimal regularization parameter insensitive to the 
   choice of the loss function?;
Univ.\ Wisconsin; 1987;

%WahbaWendelberger1980
% larry
\rhl{W}
\refJ Wahba,  G., Wendelberger, J.;
Some new mathematical methods for variational objective
analysis using splines and cross validation;
Mon.\ Wea.\ Rev.; 108; 1980; 1122--1143;

%WahbaWold1975
\rhl{W}
\refJ Wahba,  G., Wold, S.;
Periodic splines for spectral density estimation.
	 The use of cross validation for determining the
	 degree of smoothing;
Comm.\  Statist.; 4; 1975;  125--141;

%WahbaWold1975
\rhl{W}
\refJ Wahba,  G., Wold, S.;
A completely automatic French curve fitting
	 spline function by cross validation;
Comm.\ Statist.; 4; 1975;  1--17;

%WahbaWold1976
\rhl{W}
\refJ Wahba,  G., Wold, S.;
	 Histosplines with knots which are order
	 statistics;
J.  Roy.\  Statist.\  Soc.\  Ser.\ B; 38;  1976;  140--150;

%WahuBrunBouras2000
% larry 20apr00
\rhl{}
\refP Wahu, G., Brun, J. M., Bouras, A.;
Adaptive parameterization and approximation for CAD data reduction;
\Stmalod; 407--416;

%Wakoff1970
% larry
\rhl{W}
\refD Wakoff, G. I.;
Piecewise polynomial spaces and their use with the 
Rayleigh-Ritz-Galerkin method;
Harvard; 1970;

%Walden1972
\rhl{W}
\refQ Walden,  A. R.;
Quantitative comparison of automatic contouring algorithms;
(Kansas Geol Survey), xxx (ed.),  Univ.\ Kansas (Lawrence KA); 1972; 1--115;

%Waldron1994a
% shayne 26oct95
\rhl{W}
\refR Waldron, S.;
$L_p$-error bounds for Hermite interpolation;
CMS Tech.\ Rep.\ \#94-13, Center for Math.\ Sciences, U. Wisconsin-Madison;
1994; 
% has lots of information, including a photocopy of Tsumura41

%Waldron1995a
% shayne 21feb96
\rhl{W}
\refP Waldron, S; 
Symmetries of linear functionals;
\TexasVIIIa; 541--550;

%Waldron1997a
% carl 12mar97
\rhl{W}
\refJ Waldron, S.;
A multivariate form of Hardy's inequality and $L_p$-error bounds for
   multivariate Lagrange interpolation schemes;
\SJMA; 28(1); 1997; 233--258;

%Waldron1997b
% carl 10nov97
\rhl{W}
\refJ Waldron, S.;
Schmidt's inequality;
\EJA; 3(2); 1997; 117--135;
% computing the best constant in the Wirtinger-Sobolev inequality
% $\norm{f}_p\le C_{p,q,t}(b-a)^{1+1/p-1/q}\norm{Df}_q$
% for $f\in L_q^1([a,b])$ and $f(t)=0$.

%Waldron1997c
% shayne 21feb96 22may98
\rhl{W}
\refJ Waldron, S.;
Integral error formul{\ae} for the scale of mean value interpolations which 
   includes Kergin and Hakopian interpolation;
\NM; 77(1); 1997; 105--122;

%Waldron1997d
% carl 14sep95 05feb96 shayne 22may98
\rhl{W}
\refJ Waldron, S.;
$L_p$-error bounds for Hermite interpolation and the associated Wirtinger
inequalities;
\CA; 13(4); 1997; 461--679;
% Beesack's inequality

%Waldron1998
% shayne 24mar99
\rhl{W}
\refJ Waldron, S.;
Multipoint Taylor formul{\ae};
\NM; 80(3); 1998; 461--494;

%Waldron1998a
% . 14sep95, shayne 22may98
\rhl{W}
\refJ Waldron, S.;
The error in linear interpolation at vertices of a simplex;
\SJNA; 35(3); 1998; 1191--1200;
% ms, fall, 1994,
%   http://epubs.siam.org/sam-bin/dbq/article/31315

%Waldron1999
% carlrefs 20nov03
\rhl{}
\refR Waldron, Shayne;
Degree reducing interpolants for inner product spaces;
Techn.Rep., Mathematics, University of Auckland; 1999;

%Waldron2000
% carl 16aug02
\rhl{}
\refJ Waldron, Shayne;
Minimally supported error representations and approximation by the constants;
\NM; 85(3); 2000; 469--484;

%Waldron2003
% shayne 03apr06
\rhl{}
\refJ Waldron, S.;
Generalized Welch bound equality sequences are tight frames;
IEEE Trans.\ Inform.\ Theory; 49; 2003; 2307--2309;

%Waldron2009
% carl 04mar10
\rhl{W}
\refJ Waldron, Shayne;
Increasing the polynomial reproduction of a quasi-interpolation operator;
\JAT; 161; 2009; 114--126;
% generalization of HanXL2003, Boor2005a, GuessabNouisserSchmeisser2000
{\tt http://www.math.auckland.ac.nz/~waldron/Preprints/Degree-lift/degreelift.html}

%Waldron9xc
% shayne
\rhl{W}
\refJ Waldron, S.;
The error in linear interpolation at vertices of a simplex;
\SJNA; xx; 199x; xxx--xxx;

%Waldron9xd
% shayne 07may96
\rhl{W}
\refR Waldron, S.;
Error formul{\ae} for generalised Taylor interpolation;
preprint; 199x;

%Walker1950a
% .
\rhl{W}
\refB Walker,  R. J.;
Algebraic Curves;
Princeton Press (xxx); 1950;
% Springer (NY)??

%Walker1994
% larry
\rhl{W}
\refP Walker, M.;
Interpolation of an arbitrary  rectangular mesh with local control
and prescribed continuity;
\ChamonixIIb; 501--510;

%WallnerPottmann1997
% larry 10sep99
\rhl{WP}
\refP Wallner, J., Pottmann, H.;
Spline orbifolds;
\ChamonixIIIa; 445--464;

%WallnerPottmann2000
% larry 20apr00
\rhl{}
\refP Wallner, Johannes, Pottmann, Helmut;
On the geometry of sculptured surface machining;
\Stmalod; 417--432;

%Walsh1931
% . 14may99
\rhl{W}
\refJ Walsh, J. L.;
The existence of rational functions of best approximation;
TAMS; 33; 1931; 668--689;

%WalshAhlbergNilson1962
% carl:  author disorder is as is
\rhl{W}
\refJ Walsh,  J. L., Ahlberg, J. H., Nilson, E. N.;
Best approximation properties of the spline fit;
\JMM; 11; 1962;  225--234;

%WalshAhlbergNilson1965
% carl 26aug98
\rhl{W}
\refJ Walsh,  J. L., Ahlberg, J. H., Nilson, E. N.;
Best approximation and convergence properties of higher-order spline
   approximations;
\JMM; 14; 1965;  231--243;

%Walter1974
\rhl{W}
\refR Walter, V.;
Splines in Hilbert spaces;
(Proceedings of the International Conference in Functional 
Analysis and its Applications) Springer Lecture Notes 399,
Berlin, 538--560; 1974;

%Walter1992a
% carl
\rhl{W}
\refJ Walter,  Gilbert G.;
Discrete discrete wavelets;
\SJMA; 23; 1992; 1004--1014;

%Walter1992b
% carl
\rhl{W}
\refJ Walter,  Gilbert G.;
Approximation of the delta function by wavelets;
\JAT; 71(3); 1992; 329--343;
% Hermite interpolation

%Walter1993a
% carl
\rhl{W}
\refJ Walter,  Gilbert G.;
Negative spline wavelets;
\JMAA; 177; 1993; 239--253;
% develops cardinal B-splines of negative order, with B_{-1} = \delta, 
% B_{-2} := \sum_{0\le k}\delta'(\cdot-k), etc, and shows these to be
% bi-orthogonal to the corresponding B-splines of positive order.\ However,
% we know of lots of dual functionals, even for arbitrary B-splines...

%Walz1988
\rhl{W}
\refR Walz, G.;
On generalized Bernstein polynomials in CAGD;
Univ.\ Mannheim; 1988;

%Walz1989a
% carl
\rhl{W}
\refJ Walz,  G.;
Generalized planar splines;
\C; 42; 1989; 187--194;
% = Walz89b???

%Walz1989b
\rhl{W}
\refJ Walz,  G.;
On interpolation by generalized planar splines I: The polynomial case;
\C; 42; 1989; 187--194;
% = Walz89a???

%Walz1989c
% larry
\rhl{W}
\refJ Walz,  G.;
Remarks on exponential splines, in particular a contour integral representation
of exponential B-splines;
Math.\ Methods in the Applied Sciences; 11; 1989; 821--827;

%Walz1990a
\rhl{W}
\refJ Walz,  G.;
B-splines im Komplexen;
Complex Variables; 15; 1990; 90--105;

%Walz1990b
\rhl{W}
\refJ Walz,  G.;
On the solution of Beltrami's equation by complex planar splines;
Complex Variables; 15; 1990; 65--74;

%Walz1991a
\rhl{W}
\refP Walz,  G.;
Interpolation mit quadratischen Splines auf Jordan-Kurven;
\Progress; 813--819;

%Walz1991b
\rhl{W}
\refB Walz,  G.;
Spline-Funktionen im Komplexen;
B.I.-Wissenschaftsverlag (Mannheim); 1991;
% [ISBN 3-411-14651-6]

%Walz1994
% .
\rhl{W}
\refJ Walz, G.;
Asymptotic expansions for classical and generalized
divided differences including applications;
\NA; 7; 1994; 161--171;

%Walz1997a
% Tom Lyche 26aug98
\rhl{W}
\refJ Walz, G.;
Identities for trigonometric B-splines, with an
   application to curve design;
\BIT; 37; 1997; 189--201;

%Walz1997b
% Tom Lyche 26aug98
\rhl{W}
\refJ Walz, G.;
Trigonometric B\'ezier and Stancu polynomials over intervals and triangles;
\CAGD; 14; 1997; 393--397;

%Walz1998
% author 24mar99
\rhl{W}
\refJ Walz, Guido;
Splines with free knots, the heat equation, and the Gau\ss\ transform;
Comm.\ Appl.\ Anal.; 2; 1998; 169--182;

%Walz1998b
% larry 10sep99
\rhl{}
\rhl{W}
\refP Walz, G.;
Optimal bivariate crosscut segmentations;
\TexasIXc;  337--344;

%WanWLChanTFSmithB1998
% carl 20apr99
\rhl{W}
\refR Wan, W. L., Chan, Tony F., Smith, Barry;
An energy-minimizing interpolation for robust multigrid methods;
CAM report 98-5, UCLA (Los Angeles); 1998;

%WangCY1979
\rhl{W}
\refJ Wang,  C. Y.;
A spline interpolation with convexity (Chinese);
Math.\ Num.\ Sinica; 1; 1979; 233--243;

%WangCY1981
% carl
\rhl{W}
\refJ Wang, C. Y.;
Shape classification of the parametric cubic curve and parametric
 B-spline cubic curve;
\CAD; 13(4); 1981; 199--206;

%WangCY1983
% larry, carl
\rhl{W}
\refJ Wang, C. Y.;
$C^1$ rational interpolation over an arbitrary triangle;
\CAD; 15(1); 1983; 33--36;
% surface modelling.

%WangCZhang1991
\rhl{W}
\refR Wang,  C., Zhang, C.;
Cubic interpolation on triangles;
Shadong Univ., Jinan, PR China; xxx;

%WangDWKatzSzabo1982
\rhl{W}
\refR Wang, D. W., Katz, I. N., Szabo, B. A.;
Implementation of a $C^1$ triangular element based on the 
$p$-version of the finite element method;
Washington Univ.; 1982;

%WangJZ1982a
% . 14sep95
\rhl{W}
\refJ Wang, Jianzhong;
On optimal error bounds for interpolating spline;
Scienta Sinica Ser.\ A; 25; 1982; 1056--1065;
% referred to in DubeauSavoie95a

%WangJZ1982b
% . 6aug96
\rhl{W}
\refJ Wang, Jianzhong;
Optimal error $L_p$ bounds for polynomial
	 interpolating splines (Chinese);
J.  Zhejiang Univ.; 4; 1982;  98--105;

%WangJZ1982c
% . 6aug96
\rhl{W}
\refJ Wang, Jianzhong;
Quartic lacunary polynomial spline interpolation
	 of order 4 (Chinese);
J.  Math.\  Wuhan; 2; 1982;  371--378;

%WangJZ1985
\rhl{W}
\refJ Wang,  Jia Zhong;
Representations of box-splines by truncated powers;
Math.\ Numer.\ Sin.; 7; 1985; 78--89;

%WangJZ1986a
\rhl{W}
\refJ Wang,  Jian Zhong;
On the expansion coefficients in bivariate box splines;
Chinese Annals of Mathematics.\ Series A. Shuxue Niankan.\ Ji A;
7; 1986; 655--665;

%WangJZ1986b
\rhl{W}
\refJ Wang,  J.;
Biorthogonal functionals of box-splines;
Math.\ Numer.\ Sin.;  8; 1986; 75--81;

%WangJZ1987
% larry
\rhl{W}
\refJ Wang,  Jian Zhong;
On dual basis of bivariate box-spline;
\ATA; 3; 1987; 153--163;

%WangJZ9x
% . 6aug96
\rhl{W}
\refR Wang, Jianzhong;
Stability and linear independence associated with scaling vectors;
ms, April; 1996;

%WangJZChenY1989
% larry
\rhl{W}
\refP Wang,  J., Chen, Y.;
A remark on minimal supports for bivariate splines;
\TexasVI; 663--666;

%WangJZHuangD1982
% . 6aug96
\rhl{W}
\refJ Wang, Jianzhong, Huang, D.;
On quartic and quintic interpolation splines
   and their optimal error bounds;
Scientia  Sinica; 24; 1982;  1130--1141;

%WangRH1975a
\rhl{W}
\refJ Wang,  Ren-hong;
Structure of multivariate splines, and interpolation (Chinese);
Acta Math.\ Sinica; 18(2); 1975; 91--106;
% another version of the title is: The structural characterization and 
% interpolation for multivariate splines, pages 91--106. See WangRH75b
% It was translated into English by the U. Hong Kong the same year; see
% MR,56 #12709

%WangRH1975b
\rhl{W}
\refJ Wang,  R. H.;
The structural characterization and interpolation for
   multivariate splines (Chinese);
Acta Math.\ Sinica; 18(2); 1975; 91--106;

%WangRH1979
% larry
\rhl{W}
\refJ Wang,  R. H.;
On the analysis of multivariate splines in the case of
   arbitrary partition (Chinese);
Sci.\ Sinica Math.; I; 1979; 215--226;

%WangRH1980
\rhl{W}
\refJ Wang,  R. H.;
On the analysis of multivariate splines in the case of
   arbitrary partition II (Chinese);
Numer.\ Math.\ China; 2; 1980; 78--81;

%WangRH1985
\rhl{W}
\refJ Wang,  R. H.;
The dimension and basis of spaces of multivariate splines;
\JCAM; 12; 1985; 163--177;

%WangRH2000
% author 03apr06
\rhl{}
\refJ Wang, R.-H.;
Multivariate spline and algebraic geometry;
\JCAM; 121; 2000; 153--163;
% considers the space of all pp of a given smoothness on a given partition 
% generated by straight lines of some domain in R^2 as a ring under pointwise
% multiplication and investigates their zero sets aka
%  piecewise algebraic curves. 

%WangRH2001
% madcat 03apr06
\rhl{}
\refB Wang, R.-H.;
Multivariate spline functions and their applications;
Kluwer Academic Publ.{} (Dordrecht, Boston); 2001;
% this is v.529 of Mathematics and its applications
% the original Chinese version, apparently entitled `Multivariate spline and
% its applications', from Science Press (Beijing) in 1994, has the 
% additional authors: X.Q. Shi, Z.X. Luo, Z.X. Su.

%WangRHHeTXLiuXYWangSC1989
\rhl{W}
\refJ Wang,  Ren Hong, He, Tian Xiao, Liu, Xiao Yan, Wang, Shou Cheng;
An integral method for constructing bivariate spline functions;
Journal of Computational Mathematics.\ An International Journal on 
Numerical Methods, Analysis and Applications; 7; 1989; 244--261;

%WangRHLuX1988a
% .
\rhl{W}
\refJ Wang,  Ren-hong, Lu, X.;
Dimension of spline spaces over triangulations;
Scientia Sinica A; 6; 1988; 585--594;

%WangRHShiXQ1987
\rhl{W}
\refR Wang, R. H., Shi, X. Q.;
A kind of cubic $C^1$-interpolations in the $n$-dimensional 
finite element method;
Jilin Univ.; 1987;

%WangRHShiXQ1999
\rhl{W}
\refR Wang, R.-H., Shi, X.-Q.;
$S^\mu_{\mu+1}$ surface interpolations over triangulations;
Jilian Univ.; 1999;

%WangRHWangWWangSShiXQ1988
\rhl{W}
\refJ Wang, R. H., Wang, W., Wang, S., Shi, X. Q.;
The $C^1$-quadratic spline space on triangulations;
xx; xx; 1988; 123--131;

%WangRS1983
\rhl{W}
\refJ Wang,  R. S.;
On the existence and uniqueness for splines
   of order $2n-1$ with equidistant nodes;
Math.\  Numer.\ Sinica; 5; 1983;	17--24;

%WangSGWangGR1980
\rhl{W}
\refJ Wang,  S. G., Wang, G. R.;
On cubic spline interpolation for derivative values (Chinese);
J.  Shanghai Norm.\  Univ.\  Nat.\ Sci.\  Ed.; 2; 1980;  7--15;

%WangSM1999
\rhl{W}
\refR Wang,  S.-M.;
On cubic splines over non-uniform triangulations;
xxx; xxx;

%WangSMWangRH1990
\rhl{W}
\refR Wang,  S.-M., Wang, R.-H.;
The space of bivariate cubic splines on non-uniform type-2 triangulations;
xxx; xxx;

%WangSZMcAllister1984
\rhl{W}
\refR Wang, S. Z., McAllister, D. F.;
An algorithm for determining the existence of a shape 
preserving interpolatory cubic spline;
xx; 1984;

%WangT1992
% lls Lai-Schumaker book
\rhl{Wang92}
\refJ Wang, T.;
A $C^2$-quintic spline interpolation scheme on a triangulation;
\CAGD; 9; 1992; 379--386;

%WangXH1978a
% shayne
\rhl{W}
\refJ Wang, Xinghua;
The remainder of numerical differentiation formul{\ae};
Hang Zhou Da Xue Xue Bao (in Chinese); 4(1); 1978; 1--10;
% Gives a formula for the derivatives of the error in Hermite interpolation
% which involves only divided differences of order one higher than the degree
% of the polynomial space of interpolants. This is in contrast to the formula
% that one obtains simply by differentiating the error formula for Hermite 
% interpolation using the rule for differentiating a divided difference with 
% respect to one of its knots - which involves additional higher order divided
% differences. 
% The same formula was given at about the same time by %DokkenLyche78

%WangXH1978b
% . 19nov95
\rhl{W}
\refJ Wang, Xinghua;
On remainders of numerical differentiation formulas;
Ke Xue Tong Bao (in Chinese);
24(19); 1979; 869--872;

%WangXH1979a
% shayne
\rhl{W}
\refJ Wang, Xinghua;
On remainders of numerical differentiation formulas;
Ke Xue Tong Bao (in Chinese); 24(19); 1979; 869--872;
% see comments for %WangXH78  multivariate polynomial Hermite interpolation

%WangXH1979b
% . 19nov95
\rhl{W}
\refJ Wang, Xinghua;
On accurate estimations of remainders of quadrature formulas (in Chinese);
Kao Teng Hsueh Hsiao Chi Suan Shu Hsueh Hsueh Pao;
1(1); 1979; 102--111;

%WangXH1983
\rhl{W}
\refJ Wang,  X. H.;
Some notes on polynomial spline smoothing formulae (Chinese);
Math.\  Numer.\  Sinica; 5; 1983; 217--219;

%WangXHLaiMJ1986
% carl 20apr99
\rhl{W}
\refJ Wang, Xinghua, Lai,  Mingjun;
On multivariate Newtonian interpolation;
Sci.\ Sinica.\ Ser.\ A; 29(1); 1986; 23--32;

%WangXHLaiMJ2004
% carl
\rhl{}
\refJ Wang, Xinghua, Lai, Ming-Jun, Yang, Shijun;
On the divided differences of the remainder in polynomial interpolation;
\JAT; 127(2); 2004; 193--197;

%WangXHYiquanY1983
% . 19nov95
\rhl{W}
\refJ Wang, Xinghua, Yiquan, Yang;
The remainder of interpolation for the functions of low order smoothness (in 
   Chinese);
Kao Teng Hsueh Hsiao Chi Suan Shu Hsueh Hsueh Pao; 
5(3); 1983; 183--203;

%WangXLaiMJ1984
% . 10nov97 20apr99
\rhl{W}
\refJ Wang, X., Lai, Minjun;
A note to the remainder of a multivariate interpolation polynomials;
\ATA; 1(1); 1984; 57--63;

%WangYPLeeSL1998
% author 21jan02
\rhl{}
\refJ Wang, Y. P., Lee, S. L.;
Scale-space derived from B-spline;
IEEE Trans.~Pattern Analysis and Machine Intelligence;
20; 1998; 1040--1054;

%WangZBLiuQM1988
% larry 2/03 Lai-Schumaker book
\rhl{WangL88}
\refJ Wang, Z. B., Liu, Q. M.;
An improved condition for the convexity and positivity of
Bernstein--B\'ezier surfaces over triangles;
\CAGD; 5; 1988; 269--275;

%Wannebo1990a
% shayne 19may96
\rhl{W}
\refJ Wannebo, A.;
Hardy inequalities;
\PAMS; 109(1); 1990; 85--95;
% The existence of multivariate extensions of the (differential presentation)
% of Hardy's inequality

%Wannebo1994a
% shayne 19may96
\rhl{W}
\refJ Wannebo, A.;
Hardy inequalities and imbeddings in domains generalising
   $C^{0,\lambda}$ domains;
\PAMS; 122(4); 1994; 1181--1190;
% Gives the existence of multivariate Hardy's inequalities in terms
% of properties of the domain

%Ward1987
\rhl{W}
\refP Ward,  J. D.;
Polynomial reproducing formulas and the commutator of a locally supported
spline;
\Chile; 255--263;

%Waring1979
% Meijering02 20nov03
\rhl{}
\refJ Waring, E.;
Problems concerning interpolation;
Philos.\ Trans.\ R. Soc.\ London; 69; 1779; 59--67;
% First occurrence of Lagrange form of polynomial interpolant.

%Warren1993
% carlrefs 20nov03
\rhl{}
\refR Warren, Joe;
Barycentric coordinates for convex polytopes;
ms; 1993;
% generalization of construction in Wachspress75.
% uses a polynomial that is adjoint for a convex polytope
% along with the adjoints of various convex cones.

%Warren1996
% shayne 20nov03
\rhl{}
\refJ Warren, J.;
Barycentric coordinates for convex polytopes;
ACM; 6; 1996; 97--108;
% emailed shaye for details re his \ACM

%WarrenLodha1990a
% greg
\rhl{W}
\refR Warren,  J., Lodha, S.;
A B\'ezier representation for quadric surface patches;
xxx; 1990;

%WarrenWeimer1998
% carl 24mar99
\rhl{W}
\refP Warren, Joe, Weimer, Henrik;
Variational subdivision for natural cubic splines;
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%WarrenWeimer2000
% larry 20apr00
\rhl{}
\refP Warren, Joe, Weimer, Henrik;
Non-stationary subdivision for inhomogeneous order differential
   equations;
\Stmalof; 411--420;

%WasilkowskiWozniakowski1978
\rhl{W}
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Optimality of spline algorithms;
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%Wassum1989a
\rhl{W}
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$VC^1$- und $VC^2$-\"Ubergangsbedingungen zwischen
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%Waterman1999
\rhl{W}
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%Watkins1979a
\rhl{W}
\refJ Watkins, David S.;
A generalization of the Bramble-Hilbert lemma and applications to 
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\JAT; 26(3); 1979; 219--231;

%WatkinsD1976a
% .
\rhl{W}
\refJ Watkins,  D. S.;
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\IJNME; 10; 1976; 925--933;

%WatkinsD1977a
% carl
\rhl{W}
\refJ Watkins,  D. S.;
Error bounds for polynomial blending function methods;
\SJNA; 14; 1977; 721--734;

%WatkinsDLancaster1977a
% .
\rhl{W}
\refJ Watkins,  D. S., Lancaster, P.;
Some families of finite elements;
\JIMA; 19; 1977; 385--397;

%WatkinsM1988a
% ., carl
\rhl{W}
\refJ Watkins, M. A.;
Problems in geometric continuity;
\CAD; 20(8); 1988; 499--502;
% research survey.

%Watson1980
% . 03apr06
\rhl{}
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Approximation Theory and Numerical Methods;
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%WatsonBHodges1999
% . 03dec99
\rhl{W}
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Fast algorithms for rendering cubic curves;
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%WatsonDF1981
% larry 03dec99
\rhl{W}
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Computing the n-dimensional Delaunay tessellation with application to
   Voronoi polytopes;
\CJ; 24; 1981; 167--172;

%WatsonDF1982
% . 03dec99
\rhl{W}
\refJ Watson,  D. F.;
ACORD = Automatic contouring of raw data;
Computers \& Geoscience; 8; 1982; 87--101;

%WatsonDFPhillips1984
% . 03dec99
\rhl{W}
\refJ Watson,  D. F., Phillips, G. M.;
Triangle-based interpolation;
Math.\ Geol.; 16; 1984; 779--795;

%WatsonDFPhillips1985
% . 03dec99
\rhl{W}
\refJ Watson,  D. F., Phillips, G. M.;
A refinement of inverse distance weighted interpolation;
Geo.\ Proc.; 2; 1985; 315--327;

%WatsonDFPhillips1985b
% . 03dec99
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\refJ Watson,  D. F., Phillips, G. M.;
Comment on `a nonlinear empirical
   interpolation and smoothing over an irregular grid', by F.  Duggan;
Comp.\ Meth.\ Appl.\ Mech.\ Engr.; 50; 1985; 195--198;

%WatsonGG1980a
% .
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\refB Watson, G. G.;
Approximation theory and numerical methods;
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%WatsonGS1972
% author 12mar97
\rhl{W}
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Smoothing and interpolation by kriging and with splines;
Trend surface analysis and spatial correlation;
Geol.\ Soc.\ Amer., Special Paper; 146; 1972; 39--46;

%WatsonGS1984
% carl 12mar97
\rhl{W}
\refJ Watson, G. S.;
Smoothing and interpolation by kriging and with splines;
Math.\ Geol.; 16(6); 1984; 601--615;

%WatsonGS1985
% . 03dec99
\rhl{W}
\refQ Watson, G. S.;
Interpolation and smoothing of directed and undirected line data;
(Multivariate Analysis - VI), P. R. Krishnaiah (ed.), Elsevier (Amsterdam);
1985; 613--625;

%WatsonGSLeadbetter1964
% larry 03dec99
\rhl{W}
\refJ Watson, G. S., Leadbetter, M. R.;
Hazard analysis.\ I;
Biometrika; 51; 1964; 175--184;

%WatsonLTLaffeyTJHaralickRM1985
% author 03dec99
\rhl{W}
\refJ Watson, L. T., Laffey, T. J., Haralick, R. M.;
Topographic classification of digital image intensity surfaces using 
   generalized splines and the discrete cosine transformation;
\CVGIP; 29; 1985; 143--167;

%WatsonLTScottMR1987
% author 03dec99
\rhl{W}
\refJ Watson, L. T., Scott, M. R.;
Solving spline-collocation approximations to
   nonlinear two-point boundary-value problems by a homotopy method;
\AMC; 24; 1987; 333--357;

%Weber1990
% scott
\rhl{W}
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Methods for constructing curvature continuous free form surfaces;
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%WeghorstHooperGreenberg1984
\rhl{W}
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Improved computational methods for ray tracing;
\ACMTG; 3; 1984; 52--69;

%WegmanWright1983
% carl
\rhl{W}
\refJ Wegman,  Edward J., Wright, Ian W.;
Splines in Statistics;
J. Amer.\ Stat.\ Assoc.; 78(382); 1983; 351--365;

%Weierstrass1885a
% . 05feb96
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\"Uber die analytische Darstellbarkeit sogenannter willk\"urlicher Funktionen
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%Weierstrass1886a
% . 05feb96
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%Weinberger1961
% larry
\rhl{W}
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Optimal approximation for functions prescribed at
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%Weinert1972
\rhl{W}
\refR Weinert, H. L.;
A reproducing kernel Hilbert space approach to spline problems 
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%Weinert1978
% larry
\rhl{W}
\refJ Weinert,  H.;
A stochastic framework for recursive computation
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IEEE Trans.\  Inform.\  Th.; 24; 1978;  45--50;

%Weinert1978b
% larry
\rhl{W}
\refJ Weinert, H. L.;
Statistical methods in optimal curve fitting;
Commun.\ Statist.-Simula.\ Computa.; B7(4); 1978; 417--435;

%WeinertByrdSidhu1980
% larry
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\refJ Weinert,  H., Byrd, R. H., Sidhu, G. S.;
A stochastic framework for recursive computation
  of spline functions II. Smoothing splines;
J.\ Optim.\ Theory Appl.; 30; 1980; 255--268;

%WeinertDesaiSidhu1979
% larry
\rhl{W}
\refJ Weinert, H. L., Desai, U. B., Sidhu, G. S.;
ARMA splines, system inverses, and least-squares estimates;
SIAM J.\ Control Optimiz.; 17; 1979; 525--536;

%WeinertKailath1974
% larry
\rhl{W}
\refJ Weinert,  H., Kailath, J.;
Stochastic interpretations and recursive
   algorithms for spline functions;
Ann.\ Stat.; 2; 1974; 787--794;

%WeinertKailath1976
% larry
\rhl{W}
\refJ Weinert, H. L., Kailath, T.;
A spline-theoretic approach to minimum-energy control;
IEEE Trans.\ Automatic Control; AC-21; 1976; 391--393;

%WeinertSidhu1975
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\refR Weinert, H. L., Sidhu, G. S.;
Deterministic approximation by splines using stochastic 
   smoothing methods;
John Hopkins Univ.; 1975;

%WeinertSidhu1977
% larry
\rhl{W}
\refJ Weinert, H. L., Sidhu, G. S.;
On uniqueness conditions for optimal curve fitting;
J.\ Optimiz.\ Theory and Appl.; 23; 1977; 211--216;

%WeinertSidhu1999
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A spline-theoretic approach to minimum energy control Part II: 
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%Weinstein1999
\rhl{W}
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Uniform approximation through partitioning;
Univ.\ Utah; 1999;

%Weintraub1999
\rhl{W}
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Spline vs.\ Lagrange interpolation.\ Some numerical comparisons;
xx; xx;

%Welch1984a
\rhl{W}
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A technique for high performance data compression;
IEEE Computers;  17; 1984; 8--19;

%Wen1980
\rhl{W}
\refJ Wen,  T.;
A keep convex interpolation for monotonic smooth functions (Chinese);
Math.\ Num.\ Sinica; 2; 1980; 299--306;

%Wen1981
\rhl{W}
\refJ Wen,  T.;
On spline interpolation for monotone smooth functions (Chinese);
MNS; 3; 1981; 143--151;

%Wendelberger1981
\rhl{W}
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The computation of Laplacian smoothing splines with examples;
Rpt.\ 648, Dept.\ Statistics, Univ.\ Wisconsin; 1981;

%Wendelberger1982
\rhl{W}
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Smoothing noisy data with multidimensional splines and generalized
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Univ.\ Wisconsin; 1982;

%Wendelberger1982b
\rhl{W}
\refR Wendelberger, J. G.;
Estimation of divergence and vorticity using multidimensional 
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Univ.\ Wisc.; 1982;

%Wendland1997
% larry 10sep99
\rhl{W}
\rhl{W}
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Sobolev-type error estimates for interpolation by radial
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\ChamonixIIIb; 337--344;

%Wendland2005
% . 05mar08
\rhl{W}
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Scattered data approximation;
Cambridge University Press (Cambridge); 2005;

%WengHuFeng1982
\rhl{W}
\refJ Weng,  X. H., Hu, G. C., Feng, G. J.;
Error bounds for cubic Hermite splines (Chinese);
Math.\ Numer.\ Sinica; 4; 1982; 218--219;

%WengZ1982
\rhl{W}
\refJ Weng,  Z. Y.;
On the existence and uniqueness of quadratic
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Zhejiang Univ.; 4; 1982;  87--97;

%Wenz1993
% author
\rhl{W}
\refD Wenz,  H.-J.;
Ein neuer Zugang zur polynomialen Spline-Quasiinterpolation;
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%Wenz1996
% . 16aug02
\rhl{}
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Interpolation of curve data blended by generalized circles;
\CAGD; 13; 1996; 673--680;

%Wenz1997
% carl 20jun97
\rhl{W}
\refJ Wenz, Hans-J\"org;
On the limits of (linear combinations of) iterates of linear operators;
\JAT; 89(2); 1997; 219--237;
% iterates of Bernstein, Schoenberg, and Durrmeyer operators
% If $V\Lambda $ with $V:F^n\to X$ is a minimal factorization of that form
% for the lm $B$, then $\Lambda V$ represents $B$ on its range wrto the 
% basis $V$, hence the limiting behavior of the sequence $(B^k: 
% k=0,1,2,\ldots)$ can be entirely understood from the that of the matrix 
% sequence $((\Lambda V)^k)$.

%Werner1974a
% author 26aug98
\rhl{W}
\refJ Werner, H.;
Tschebyscheff-Approximation mit einer Klasse rationaler 
   Spline-Funktionen;
\JAT; 10; 1974; 74--92;

%Werner1974b
% author 26aug98
\rhl{W}
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Tschebyscheff-Approximation mit nichtlinearen Spline-Funktionen;
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%Werner1975
% author 26aug98
\rhl{W}
\refJ Werner, H.;
Interpolation and integration of initial value problems of ordinary
   differential equations by regular splines;
\SJNA; 12; 1975; 255--271;

%Werner1976
% author 26aug98
\rhl{W}
\refP Werner, H.;
Numerische Behandlung gew\"ohnlicher Differentialgleichungen mit Hilfe von
   Splinefunktionen;
\Clausthal; 167--175;

%Werner1978
% http://www.math.technion.ac.il/hat/fpapers/wernercombio.pdf
\refJ Werner, H.;
Neuere Entwicklungen auf dem Gebiet der nichtlinearen Splines; 
\ZAMM; 58(6); 1978; 86--95;
%Schriftenreihe No. 26, Rechenzentrum Universit\"at M\"unster (M\"unster, 
%Germany); 1977;

%Werner1979a
% carl 26aug98
\rhl{W}
\refP Werner, H.;
An introduction to non-linear splines;
\Sahney; 247--306;

%Werner1980a
% carl
\rhl{W}
\refJ Werner,  H.;
Remarks on Newton--type multivariate interpolation for subsets of grids;
\C; 25; 1980; 181--191;
% polynomial (and even Chebyshev-set) interpolation on a lower set of a
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%  %DelvosPosdorf77, 79. Includes an error expression due to R. Haverkamp
% which looks like the one in IsaacsonKeller66, it's not symmetric and,
% for tensor products, involves that next highest mixed derivative. 

%Werner1980b
% larry
\rhl{W}
\refP Werner, H.;
Approximation by regular splines with free knots;
\TexasII; 567--573;

%Werner1980c
% http://www.math.technion.ac.il/hat/fpapers/wernercombio.pdf
\refP Werner, H.;
The development of nonlinear splines and their applications;
\TexasIII; 125--150;

%WernerLoeb1976
% author 26aug98
\rhl{W}
\refP Werner, H., Loeb, H.;
Tschebyscheff-Approximation by regular splines with free knots;
\BonnI; 439--452;

%Wertenbruch1978
\rhl{W}
\refR Wertenbruch,  S.;
Ein Blending-Verfahren zur L\"osung spezieller
Probleme der zwei dimensionalen Interpolation;
Diplomarbeit, Bonn; 1978;

%Westgaard1991
\rhl{W}
\refR Westgaard, G.;
Spline modellering av et hode;
Univ.\ Oslo; 1991;

%WheedenZygmund1977a
% . 26oct95
\rhl{W}
\refB Wheeden, R. L., Zygmund, A.;
Measure and integral;
Marcel Dekker, Inc.{} (New York); 1977;
% An introduction to real analysis

%WheelerYotov1998
% larry 10sep99
\rhl{}
\rhl{W}
\refP Wheeler, M. F.,  Yotov, I.;
Mortar mixed finite element approximations for elliptic and
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\TexasIXc; 377--392;

%Whelan1986
% greg
\rhl{W}
\refJ Whelan,  T.;
A representation of a $C^2$ interpolant over triangles;
\CAGD; 3; 1986; 53--66;

%White1948
% larry
\rhl{W}
\refJ White, A.;
Interlocking interpolation curves;
Trans.\ Actuarial Soc.\ Americ.; 49; 1948; 337--364;

%WhiteWhiteley1983
% larry
\rhl{W}
\refJ White,  N. L., Whiteley, W.;
The algebraic geometry of stresses in frameworks;
\SJADM; 4; 1983; 481--511;

%Whiteley1982
\rhl{W}
\refR Whiteley,  W.;
Motions and stresses of projected polyhedra;
Cornell Univ.; 1982;

%Whiteley1982b
% larry
\rhl{W}
\refJ Whiteley, W.;
Motions and stresses of projected polyhedra;
Structural Topology; 7; 1982; 13--38;

%Whiteley1986
\rhl{W}
\refR Whiteley,  W;
The analogy between multivariate splines and hinged panel structures;
Champlain Regional College, Qu\'ebec; 1986;

%Whiteley1989a
% larry
\rhl{W}
\refJ Whiteley,  W.;
Rigidity and polarity II: Weaving lines and tensegrity frameworks;
Geometriae Dedicata; 30; 1989; 255--279;

%Whiteley1989b
\rhl{W}
\refJ Whiteley,  W.;
A matroid on hypergraphs, with applications in scene analysis and geometry;
Discrete and Computational Geometry; 4; 1989; 75--95;

%Whiteley1989c
\rhl{W}
\refR Whiteley,  W;
Matroids and rigid structures;
Champlain Regional College, Qu\'ebec; 1989;

%Whiteley1990a
% carlrefs
\rhl{W}
\refR Whiteley,  W;
The geometry of bivariate $C_2^1$-splines;
Champlain Regional College, Qu\'ebec; 1990;

%Whiteley1991a
% peter carlrefs
\rhl{W}
\refQ Whiteley,  W.;
The combinatorics of bivariate splines;
(Applied Geometry and Discrete Mathematics, Victor Klee Festschrift),
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567--608;

%Whiteley1991b
% peter carlrefs
\rhl{W}
\refP Whiteley,  W.;
A matrix for splines;
\Progress; 821--828;
% dimension of spline spaces

%Whiteley1991c
% peter
\rhl{W}
\refJ Whiteley,  W.;
Vertex splitting in isostatic frameworks;
Structural Topology; 16; 1991; 23--30;

%Whiten1971
% larry
\rhl{W}
\refJ Whiten,  W. J.;
The use of multi-dimensional cubic spline functions for
regression and smoothing;
Austral.\ Computer J.; 3; 1971; 81--88;

%Whiten1972
\rhl{W}
\refJ Whiten,  W. J.;
The use of periodic spline functions for regression
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Austral.\  Comput.\  J.; 4; 1972; 31--34;

%Whitney1957
% carl 23jun03
\rhl{}
\refJ Whitney, Hassler;
On functions with bounded $n$th differences;
\JMPA (9); 36; 1957; 67--95;

%Whitney1959
% carl 23jun03
\rhl{}
\refJ Whitney, Hassler;
On bounded functions with bounded $n$th differences;
\PAMS; 10; 1959; 480--481;

%WhitneyH1934
% carl 15jan99
\rhl{W}
\refJ Whitney,  H.;
Analytic extensions of differentiable functions defined on closed sets;
\TAMS; 36; 1934; 63--89;

%WhitneyH1934b
% carl 26aug98
\rhl{W}
\refJ Whitney,  H.;
Differentiable functions defined in closed sets. I;
\TAMS; 36; 1934; 369--387;

%WhitneyH1992
% MR 26aug98
\rhl{W}
\refB Whitney, Hassler;
Collected Papers, I and II;
(edited by James Eells and Domingo Toleda), Birkh\"auser Boston, Inc.
(Boston MA); 1992;

%Whittaker1915
% . 20nov03
\rhl{}
\refJ Whittaker, E. T.;
On the functions which are represented by the expansions of
   interpolation-theory;
\PRSEA; 35; 1915; 181--194;
% Whittaker cardinal series (Borel99 already has this infinite sum)

%Whittaker1923
\rhl{W}
\refJ Whittaker,  E. T.;
On a new method of graduation;
\PEMS; 41; 1923; 63--75;

%Whittaker1935
% carl 21nov08
\rhl{W} 
\refB Whittaker,  E. T.;
Interpolatory function theory;
Cambridge Univ.\ Press (New York, London); 1935;

%WhittakerRobinson1923
% Meijering02 20nov03
\rhl{}
\refB Whittaker, E. T., Robinson, G.;
A Short Course in Interpolation;
Blackie (Glasgow, UK); 1923;

%WhittakerRobinson1937a
% carlrefs
\rhl{WR}
\refB Whittaker, E. T., Robinson, G.;
The Calculus of Observations, A Treatise on Numerical Mathematics, 2nd ed.;
Blackie (Glasgow, UK); 1937;

%Whitten1973
\rhl{W}
\refJ Whitten,  E. H. T., Koelling, M. E. V.;
Spline surface interpolation, spatial filtering, and
trend surfaces for geologically mapped variables;
Math.\ Geol.; 5; 1973; 111--126;

%Whitten1974
\rhl{W}
\refR Whitten, E. H. T.;
Orthogonal-polynomial contoured trend-surface maps for 
irregularly-spaced data;
Nothwestern Univ.; 1974;

%Whitten1974b
% larry
\rhl{W}
\refJ Whitten, E. H. T.;
Scalar and directional field and analytical data for spatial 
variability studies;
Math.\ Geology; 6; 1974; 183--198;

%Whitten1999
\rhl{W}
\refR Whitten, E. H. T.;
The practical use of trend-surface analyses in the geological 
sciences; 282--297; xx;

%WhittenKoelling1973
% larry
\rhl{W}
\refJ Whitten,  E. H. T., Koelling, M. E. V.;
Geological use of multidimensional spline functions;
Math.\ Geol.; 5; 1973; XX;

%WhittenKoelling1974
\rhl{W}
\refR Whitten,  E. H. T., Koelling, M. E. V.;
Computation of bicubic-spline surfaces for irregularly
spaced data;
Rpt.\ 3, Northwestern Univ.; 1974;

%Wick1986a
% greg
\rhl{W}
\refJ Wick,  J. J. van;
Bicubic patches for approximating non-rectangular control
-point meshes;
\CAGD; 3; 1986; 1--13;

%Wickerhauser1994a
% . 20feb96
\rhl{W}
\refB Wickerhauser, M. V.;
Adapted Wavelet Analysis from Theory to Software;
A. K. Peters (Wellesley MA); 1994;

%Widder1941
% shayne 22may98
\rhl{W}
\refB Widder, D. V.;
The Laplace transform;
Princeton University Press (Princeton); 1941;

%Widder1972
\rhl{W}
\refB Widder,  D. V.;
The Laplace Transform; 
Princeton University Press, 8th printing (Princeton); 1972;

%Widlund1971
\rhl{W}
\refJ Widlund, O. B.;
Results on best possible error bounds for finite element 
methods and approximation with piecewise polynomial functions;
Lecture Notes in Mathematics; 228; 1971; 253--263;

%Widlund1977
% carl
\rhl{W}
\refJ Widlund, Olof B.;
On best error bounds for approximation by piecewise polynomial functions;
\NM; 27; 1977; 327--338;

%Wilf1964
% larry
\rhl{W}
\refJ Wilf,  H. S.;
The stability of smoothing by least squares;
\PAMS; 15; 1964; 933--937;

%Wilhelmsen1974
% LLS Lai-Schumaker book
\rhl{Wil74}
\refJ Wilhelmsen, D. R.;
A Markov inequality in several dimensions;
\JAT; 11; 1974; 216--220;

%WillemansDierckx1992
% carlrefs 20nov03
\rhl{}
\refR Willemans, Karin, Dierckx, Paul;
Surface fitting using convex Powell-Sabin splines;
Kath.~U.\ Leuven, dept.{} c.s., report TW 177; 1992;

%WillemansDierckx1993
\rhl{W}
\refR Willemans, K., Dierckx, P.;
Surface fitting with boundary conditions by means of Powell-Sabin
splines;
TW 199, K.\ U.\ Leuven; 1993;

%WillemansDierckx1994
% larry
\rhl{W}
\refP Willemans, K., Dierckx, P.;
Constrained surface fitting using Powell-Sabin splines;
\ChamonixIIb; 511--520;

%Williams1986
% carl
\rhl{W}
\refP Williams,  C. J. K.;
Defining and designing flexible tensile surface structures;
\SurfacesI; 143--177;

%WilsonGoodrichSpratte1988
\rhl{W}
\refR Wilson, F. W., Goodrich, R. K., Spratte, W;
Lawson's triangulation is nearly optimal for controlling error 
bounds; xx; 1988;

%WilsonTaylorDohertyGhaboussi1973a
% . 26oct95
\rhl{W}
\refQ Wilson, E. L., Taylor, R. L., Doherty, W. P., Ghaboussi, J.;
Incompatible displacement models;
(Numerical and Computer Methods in Structural Mechanics),
S. J. Fenves, N. Perrone, A. R. Robinson, W. C. Schnobrich (eds.),
Academic Press (New York); 1973; 43--57;
% The Wilson's brick finite element 
% It involves integrals of derivatives - as does Fraeijs de Veubeke triangle

%Wind1977
\rhl{W}
\refJ Wind,  H.;
The rounded cubic spline;
\JIMA; 19; 1977;  441--445;

%Winkler1997
% larry 10sep99
\rhl{W}
\rhl{W}
\refP Winkler, J. R.;
Numerically stable conversion between the B\'ezier and B-spline
forms of a curve;
\ChamonixIIIa; 465--472;

%Wittenbrink1973
% carl 22may98
\rhl{W}
\refJ Wittenbrink, K. A.;
High order projection methods of moment- and collocation-type for nonlinear
   boundary value problems;
\C; 11; 1973; 255--274;

%Wixom1975
\rhl{W}
\refR Wixom, J. A.;
Blending-function interpolation over non-rectangular domains;
GMR-1957; 1975;

%Wold1974
\rhl{W}
\refJ Wold,  S.;
Spline functions in data  analysis;
Technometrics; 16; 1974;  1--11;

%Wolf1981
\rhl{W}
\refJ Wolf,  H.;
Multiquadratische Methode und Kollokation;
Allgemeine Ver\-messungs-Nachrichten; XX; 1981; 89--95;

%Wolter1985
% larry
\rhl{W}
\refD Wolter,  F.-E.;
Cut loci in bordered and unbordered Riemannian manifolds;
TU Berlin; 1985;

%Wolter1992
\rhl{W}
\refR Wolter,  F.-E.;
Cut locus and medial axis in global shape interrogation and representation;
MIT Cambridge, Memorandum 92-2; 1992;

%Wolter1999
\rhl{W}
\refR Wolter,  F.-E.;
Interior metric shortest paths and loops in Riemannian manifolds with 
not necessarily smooth boundary;
xxx; xxx;

%WolterTuohy1991a
\rhl{W}
\refR Wolter,  F.-E., Tuohy, S. T.;
Approximation of high degree and procedural curves;
Design Laboratory Memorandum 90-8, MIT, Cambridge; 1991;

%WolterTuohy1991b
\rhl{W}
\refR Wolter,  F.-E., Tuohy, S. T.;
Curvature computations for degenerate surface patches;
Design Laboratory Memorandum 91-15, MIT, Cambridge; 1991;

%Wolters1992
\rhl{W}
\refR Wolters, H. J.;
A Newton-type method for computing best segment approximations;
Arizona State Univ.; 1992;

%Wolters2000
% larry 20apr00
\rhl{}
\refP Wolters, Hans J.;
Extensions: extrapolation methods for CAD;
\Stmalod; 433--441;

%Woltring1985
% larry
\rhl{W}
\refJ Woltring, H. J.;
On optimal smoothing and derivative estimation from noisy 
displacement data in biomechanics;
Human Movement Sc.; 4; 1985; 229--245;

%Woltring1986
% larry
\rhl{W}
\refJ Woltring, H. J.;
A Fortran package for generalized, cross-validatory spline 
smoothing and differentiation;
Adv.\ Eng.\ Software; 8; 1986; 104--113;

%Wong1984
% carl
\rhl{W}
\refJ Wong,  Wing Hung;
On constrained multivariate splines and their approximations;
\NM; 43; 1984; 141--152;

%WongAgarwal1989
% larry
\rhl{W}
\refJ Wong,  P. J. Y., Agarwal, R. P.;
Explicit error estimates for quintic and biquintic spline interpolation;
\CMA; 18; 1989; 701--722;

%WongAgarwal1999
\rhl{W}
\refR Wong,  P. J. Y., Agarwal, R. P.;
Quintic spline solutions of Fredholm integral equations of the second kind;
Annal.\ Polonici Mathematici; 19xx;

%Woo1983
\rhl{W}
\refR Woo, T. C.;
Topological integrity in 3D triangulation;
Univ.\ Michigan; 1983;

%Woodford1969
% larry
\rhl{W}
\refJ Woodford,  C. H.;
Smooth curve interpolation;
\BIT; 9; 1969;	69--77;

%Woodford1970
% larry
\rhl{W}
\refJ Woodford,  C. H.;
An algorithm for data smoothing using spline functions;
\BIT; 10; 1970;  501--510;

%Woodward1986a
% carl
\rhl{W}
\refP Woodward,  L. M.;
Elementary exposition of differential forms;
\SurfacesI; 74--93;

%Woodward1986b
% carl
\rhl{W}
\refP Woodward,  L. M.;
Differential forms in the theory of surfaces;
\SurfacesI; 96--115;

%WorobelKuzhiiPopov1982
\rhl{W}
\refJ Worobel,  R. A., Kuzhii, L. I., Popov, B. A.;
Nonlinear uniform splines (Russian);
Otbor i Peredacha Inform.; 66; 1982; 33--40;

%Worsey1984
% greg
\rhl{W}
\refJ Worsey,  A. J.;
A modified $C^2$ Coon's patch;
\CAGD; 1; 1984; 357--360;

%Worsey1985
% greg
\rhl{W}
\refJ Worsey,  A. J.;
$C^2$ interpolation over hypercubes;
\CAGD; 2; 1985; 107--115;

%WorseyFarin1987
% greg
\rhl{W}
\refJ Worsey,  A. J., Farin, G.;
An $n$--dimensional Clough-Tocher interpolant;
\CA; 3; 1987; 99--110;

%WorseyPiper1988
% greg
\rhl{W}
\refJ Worsey,  A. J., Piper, B.;
A trivariate Powell-Sabin interpolant;
\CAGD; 5; 1988; 177--186;

%Wright1977
\rhl{W}
\refR Wright, I. W.;
Splines in statistics;
Univ.\ North Carolina; 1977;

%WrightWegman1980
% larry
\rhl{W}
\refJ Wright,  I. W., Wegman, E. J.;
Isotonic,  convex and related splines;
Ann.\ Statist.; 8(5); 1980;  1023--1035;
% constrained spline approximation, shape preserving

%Wronicz1975
\rhl{W}
\refJ Wronicz,  Z.;
On the approximation and interpolation by
	 mulitiple splines;
Prec.\  Mat.\  Zeszyt.; 17;  1975;  147--157;

%Wu1988a
% ,
\rhl{W}
\refJ Wu,  Zheng-Cheng;
Error bounds for the Bernstein polynomial on the $n$-dimensional simplex
(Chinese);
XXX (A); 6; 1988; 298--304;
% referred to in JiaWu88

%WuAbelGreenberg1977
% larry
\rhl{W}
\refJ Wu,  S., Abel, J. F., Greenberg, D.;
An interactive computer graphics approach to surface representation;
\CACM; 20; 1977; 703--712;

%WuDB1993
% larry 2/03 Lai-Schumaker book
\rhl{Wu93}
\refJ Wu, D. B.;
Dual bases of a Bernstein polynomial basis on simplices;
\CAGD; 10; 1993; 483--489;

%WuSha1981
\rhl{W}
\refJ Wu,  Z. Ch., Sha, Z.;
On interpolation by splines in imaginary
	 tension (Chinese);
Numer.\ Math.\  J.  Chinese  Univ.; 3; 1981;  373--378;

%WuZM1988
\rhl{W}
\refJ Wu,  Zong-Min;
A suitable method for the interpolation of multivariate scattered data, 
and its convergence rate;
Chinese Quarterly Journal of Mathematics; 3; 1988; 105--110;

%WuZM1992
% .
\rhl{W}
\refJ Wu, Zong-min;
Hermite-Birkhoff interpolation of scattered data by radial basis functions;
\JATA; 24; 1992; 201--215;

%WuZMSchaback1993
% . 10nov97
\rhl{W}
\refJ Wu,  Zong-min, Schaback, R.;
Local error estimates for radial basis function interpolation
   to scattered data;
\IMAJNA; 13; 1993; 13--27;
% preprint 1990

%WuZMSchaback1999
\rhl{W}
\refR Wu,  Zong-min, Schaback, R.;
Shape preserving properties and convergence of univariate multiquadric 
quasi-interpolation;
xxx; xxx;

%Wulbert1992
% carl
\rhl{W}
\refJ Wulbert,  D.;
Oscillation spaces;
\JAT; 69; 1992; 188--204;

%Wulbert1999
% carl 24mar99
\rhl{W}
\refJ Wulbert, Daniel;
Interpolation at a few points;
\JAT; 96(1); 1999; 139--148;
% simplifies and extends Shekhtman95