%Vagans1972
\rhl{V}
\refJ Vagans,  A. A.;
On a smooth piecewise polynomial approximation method;
Latvian Math.\  Yearbook II,  Izdat.\ Zinatne Riga; XX; 1972;  15--23;

%Vakarchuk1983
\rhl{V}
\refJ Vakarchuk,  S. B.;
On spline curve-aided approximation of curves
	 preset in a parametric form (Russian);
Ukrain	Mat.\  J.; 35; 1983;  352--355;

%Vakarchuk1983b
\rhl{V}
\refJ Vakarchuk,  S. B.;
Approximation of curves and surfaces by
	 splines (Russian);
Akad.\  Nauk.\  Ukrain SSSR, Inst.\  Mat.;  32; 1983;  1--48;

%VanArman1968
\rhl{V}
\refR VanArman, D. J.;
Classification of experimental designs relative to polynomial spline
regression functions;
Purdue; 1968;

%VanDeVilleBluUnserPhilipsLemahieuVandeWalle2004
% carl 03apr06
\rhl{}
\refJ Van De Ville, D., Blu, T., Unser, M., Philips, W., Lemahieu, I., Van de
Walle, R.;
Hex-splines: A novel spline family for hexagonal lattices;
IEEE Trans.\ Image Proc.; 13(6); 2004; 758--772;
% B-splines for hexagonal meshes

%VanWijk1986
% carl
\rhl{V}
\refJ Wijk,  J. J. Van;
Bicubic patches for approximating non-rectangular
con\-trol-point meshes;
\CAD; 3; 1986; 1--13;

%Varady1982
% larry
\rhl{V}
\refJ V\'arady, T.;
An experimental system for interactive design and manufacture of
sculptured surfaces;
Computers in Industry; 3; 1982; 125--135;

%Varah1977
% carl
\rhl{V}
\refJ Varah, J. M.;
On the condition number of local bases for
	 piecewise cubic polynomials;
\MC; 31(137); 1977; 37--44;

%Varas1984
\rhl{V}
\refR Varas, M. L.;
A dual algorithm for the computation of the monotone cubic spline;
Santiago; 1984;

%Varas1987
% larry
\rhl{V}
\refJ Varas, M. L.;
On the computation of the monotone cubic spline function;
\JATA; 3; 1987; 91--105;

%Varga1969
\rhl{V}
\refP Varga,  R. S.;
Error bounds for spline interpolation;
\MadisonII; 367--388;

%Varga1971
% carl 22may98
\rhl{V}
\refB Varga, R. S.;
Functional Analysis and Approximation Theory in Numerical Analysis;
CBMS Vol.~3, SIAM (Philadelphia PA); 1971;

%Varga1976
\rhl{V}
\refJ Varga,  R. S.;
On diagonal dominance arguments for bounding $\|A^{-1}\|_\infty$;
\LAA; 14; 1976; 211--217;

%VargasRodriguezFlicknerSanz1992
% .
\rhl{V}
\refR Vargas, D. C., Rodriguez, E. J., Flickner, M., Sanz, J. L.;
Splines and spline fitting revisited;
IBM Research Report RJ8261; 1992;

%Varma1978
\rhl{V}
\refJ Varma,  A. K.;
Lacunary interpolation by splines I. (0,4)-cases;
Acta Math.\  Acad.\  Sci.\  Hung.; 31; 1978; 185--192;

%Varma1978b
\rhl{V}
\refJ Varma,  A. K.;
Lacunary interpolation by splines II. (0,1,3)-cases;
Acta Math.\  Acad.\  Sci.\  Hung.;  34; 1978; 193--203;

%VarmaKatsifarakis1987a
% Shayne 05feb96
\rhl{V}
\refJ Varma, A. K., Katsifarakis, K. L.;
Optimal error bounds for Hermite interpolation;
JAT; 51; 1987; 350--359;
% Yet another special case of Shadrin's result
% This time for Hermite interpolation by cubics to function
% value and derivative at the endpoint of the interval
%

%VarmaYu1991
\rhl{V}
\refJ Varma, A. K., Yu, Xiang Ming;
% larry
Pointwise estimates for an interpolation process of S.~N. Bernstein;
\JAMSA; 51; 1991; 284--299;

%VarmaYu1999
\rhl{V}
\refJ Varma,  A. K., Yu, X. M.;
Pointwise estimates for an interpolation process of S. N. Bernstein;
Australian J. Math.; xxx; to appear; xxx;

%Vasilenko1969
\rhl{V}
\refJ Vasilenko,  Yu.\ V.;
On an optimal piecewise linear approximation of
functions of several variables (Russian);
Automatyka; XX; 1969; 28--35;

%Vasilenko1983a
% carl 14sep95
\rhl{V}
\refB Vasilenko, V. A.;
Spline Functions: Theory, Algorithms, Programs (in Russian);
Akad.\ Nauk SSSR, Novosibirsk Computing Center (Novosibirsk); 1983;

%VasilievAA1981
\rhl{V}
\refJ Vasiliev,  A. A.;
Approximation by interpolatory splines of arbitrary
	 deficiency;
\MaZ; 29; 1981;  743--748;

%VasilievAAMalozemovPevnyi1979
\rhl{V}
\refJ Vasiliev,  A. A., Malozemov, V. N., Pevnyi, A. B.;
Interpolation and approximation by spline functions
  of an arbitrary defect;
Vestnik Leningrada Univ.; 4; 1979; 23--30;

%VasilievVA1992
% carl 6aug96
\rhl{V}
\refJ Vasil'ev, V. A.;
On function spaces that are interpolating at any $k$ nodes;
Functionalnyi Analiz i ego Prilozhenia; 26(3); 1992; 72--74;
% see Vasiliev94a

%VasilievVA1994a
% carl 14sep95
\rhl{V}
\refB Vasiliev, V. A.;
Complements of Discriminants of Smooth Maps: Topology and Applications,
   Revised Edition;
Amer.\ Math.\ Soc.\ Transl.\ of Math.\ Monographs vol.\ 98 (Providence RI);
1994; 
% contains discussions of, and references to, Vassiliev's work on the smallest
% dimension I(M,k) of a linear subspace of the space of continuous functions on 
% some manifold which contains interpolants to arbitrary data at arbitrary k 
% points from that manifold. Examples: I(S^1,k) = 2floor{k/2}+1.
% k+i(k) \le I(\RR^2,k) \le 2k-1, with  i(k) := number of 1's in binary
% expansion of k-1, and with  \Pi_1 + span(()^{2,0} + ()^{0,2})  a good space
% for k=3.

%Vaughan1999
\rhl{V}
\refJ Vaughan, H.;
Some notes on interpolation;
xx; xx; xx; 482--497;

%VedeneevZhidkovShchedrin0
% larry
\rhl{V}
\refJ Vedeneev, E. P., Zhidkov, N. P., Shchedrin, B. M.;
Differentiation of a tabular function by the method of interpolating
conjugation;
USSR Comput.\ Math.\ and Math.\ Phys.; 10; 1970; 200--207;

%Vegter1998
% carlrefs 20nov03
\rhl{}
\refR Vegter, G.;
The apolar bilinear form in geometric modeling;
IWI-preprint 98-9-01, Comp.Sci., University of Groningen; 1998;
% multivariate polynomials

%Veldhuizen1986
% carl
\rhl{V}
\refR Veldhuizen, M. van;
On polygonal approximations of an invariant curve;
Tech.\ Report WS314, Dept.\ Math.\ Comput.\ Sci., Universiteit Amsterdam; 1986;
% and Math. Comput., submitted for publication, 
% ref. in \JCAM 21, 1988, 212

%Veldhuizen1988
% carl
\rhl{V}
\refJ Veldhuizen, M. van;
Convergence results for invariant curve algorithms;
\MC; 51(184); 1988; 677--697;
% norm of cubic spline interpolant is bounded by 1 + 3(local mesh ratio)^2
% and, for uniform knots, is bounded below by 11/8.

%Velho1992
\rhl{V}
\refR Velho,  L.;
B-spline pyramid: A multiscale piecewise representation for implicit objects;
Univ.\ of Toronto; 1992;

%Velikin1970
\rhl{V}
\refJ Velikin, V. L.;
Best approximations of continuous functions by spline functions;
Math.Notes; xx; 1970; 492--495;

%Velikin1972
\rhl{V}
\refJ Velikin,  V. L.;
Approximation by cubic splines in the classes
	 of continuously differentiable functions;
\MaZ; 11; 1972;	215--226;

%Velikin1987
% . 12mar97
\rhl{V}
\refJ Velikin, V. L.;
On the asymptotic relation between the approximation methods of the periodic
   function by splines and trigonometric polynomials;
Anal.\ Math.; 13; 1987; 45--87;

%VelikinKorneichuk1971
% larry
\rhl{V}
\refJ Velikin, V. L., Korneichuk, N. P.;
Accurate estimates of deviations of spline approximations to classes of 
differentiable functions;
Math.\ Notes; 9; 1971; 278--284;
% from \MaZ; 9; 1971;  483--494;

%Verde-Star1991
% zb 25mar11
\rhl{V}
\refJ Verde-Star, Luis;
Divided differences and combinatorial identities;
Stud.\ Appl.\ Math.; 85(3); 1991; 215--242;
% intro plus identities

%Verde-Star1999
\rhl{V}
\refJ Verde-Star, L.;
An algorithm for the inversion of generalized Vandermonde matrices;
\CA; xx; xx; xx--xx;

%VerdeStar1991
% zb 23jun03
\rhl{}
\refJ Verde-Star, Luis;
Divided differences and combinatorial identities;
Stud.\ Appl.\ Math.; 85(3); 1991; 215--242;
% intro plus identities
% see ChenWLouck96a

%VerdeStar1995
% carlrefs 20nov03
\rhl{}
\refJ Verde-Star, Luis;
Biorthogonal polynomial bases and Vandermonde-like matrices;
Studies Appl.\ Math.; 95; 1995; 269--295;

%VergeestDijk1999
\rhl{V}
\refR Vergeest,  J. S. M., Dijk, C. G. C. van;
B-spline surfaces for real time shape design;
Delft Univ.\ of Technology; xxx;

%VerlindenCools1992
% carl
\rhl{V}
\refJ Verlinden,  P., Cools, R.;
On cubature formulae of degree $4k+1$ attaining M\"oller's lower bound for
integrals with circular symmetry;
\NM; 61; 1992; 395--408;

%VerlindenHaegemans1992
% sherm, update  page numbers
\rhl{V}
\refJ Verlinden,  P., Haegemans, A.;
An asymptotic expansion in wavelet analysis
and its application to accurate numerical wavelet decomposition;
\NA; 2; 1992; 287--298;

%VermeulenBartelsHeppler1992
% sherm, pagination update, refJb to refJc
\rhl{V}
\refJ Vermeulen,  A. H., Bartels, R. H., Heppler, G. R.;
Integrating Products of B-Splines;
\SJSSC; 13(4); 1992; 1025--1038;

%VeronRisMusse1976a
% carl
\rhl{V}
\refJ Veron, M., Ris, G., Musse, J.-P.;
Continuity of biparametric surface patches; 
\CAD; 8(4); 1976; 267--273;

%Vershinin1981
\rhl{V}
\refJ Vershinin,  V. V.;
Derivatives of smoothing splines (Russian);
Vycisl.\  Systemy; 87; 1981;  35--42;

%Vershinin1981b
\rhl{V}
\refJ Vershinin,  V. V.;
Spline mappings Russian;
Vycisl.\  Systemy; 87; 1981;  43--52;

%VershininPavlov1988
% larry
\rhl{V}
\refJ Vershinin,  V. V., Pavlov, N. N.;
Splines in a convex set and the problem of numerical differentiation;
U.S.S.R.\ Comput.\ Maths.\ Math.\ Phys.; 27; 1987; 199--202;

%Versprille1975
\rhl{V}
\refD Versprille,  K. J.;
Computer-Aided Design Applications of the Rational B-Spline 
Approximation Form;
Syracuse University; 1975;
% first(?) appearance of NURBS

%Vertesi1989
% .
\rhl{V}
\refJ V\'ertesi, P.;
Hermite-Fej\'er interpolations of higher order, I;
\AMASH; 54; 1989; 135--1529;

%Vertesi1990a
% .
\rhl{V}
\refJ V\'ertesi, P.;
Hermite-Fej\'er interpolations of higher order, II (mean convergence);
\AMASH; 56; 1990; 369--380;

%Vertesi1990b
% author 23jun03
\rhl{V90}
\refJ V\'ertesi, P.;
Optimal Lebesgue constants for Lagrange interpolation;
\SJNA; 27; 1990; 1322--1331;

%Vertesi1999
% carl 26aug99
\rhl{V}
\refJ V{\'e}rtesi, P.;
On the Lebesgue function of weighted Lagrange interpolation. I. (Freud-type
   weights);
\CA; 15(3); 1999; 355--368;

%Vertesi2002
% author 23jun03
\rhl{V}
\refJ V{\'e}rtesi, P.;
On the Lebesgue function and Lebesgue constant: A tribute to Paul Erd\H os;
Bolyai Soc.\ Math.\ Studies; 11; 2002; 705--728;

%Vesely1977
\rhl{V}
\refJ Vesely,  V.;
An algorithm for the computation of polynomial
	 splines of odd degree;
Kybernetika; 13; 1977; 282--289;

%Vesprille1975
% farin 03apr06
\rhl{}
\refD Vesprille, K.;
Computer aided design applications of the rational
   {B-}spline approximation form;
Syracuse Univ.; 1975;
% first paper on rational splines

%Vetterli1986
\rhl{V}
\refJ Vetterli,  M.;
Filter bank allowing perfect reconstruction; 
{Signal Processing}; 10; 1986; 219--244;

%Videnskii1951
% shadrin 03apr06
\rhl{}
\refJ Videnskii, V. S.;
On estimates of derivatives of a polynomial (Russian);
Izv.\ Akad.{} Nauk SSSR Ser.\ Mat.; 15; 1951; 401--420;

%VigoNuriaCotria2002
% larry Lai-Schumaker book
\rhl{VigNC02}
\refJ Vigo, M., N\'uria, P., Cotria, J.;
Regular triangulations of dynamic sets of points;
\CAGD; 19; 2002; 127--149;

%VigoPlaBrunet1997
% larry 10sep99
\rhl{VPB}
\rhl{V}
\refP Vigo, M., Pla, N., Brunet, P.;
From degenerate patches to triangular and trimmed patches;
\ChamonixIIIa; 435--444;

%Villalobos1983
% larry
\rhl{V}
\refR Villalobos, M. A.;
Estimation of posterior probabilities using multivariate smoothing
splines and generalized cross-validation;
Univ.\ Wisc.; 1983;

%VillalobosWahbaXX
\rhl{V}
\refJ Villalobos,  M. A., Wahba, G.;
Inequality constrained multivariate smoothing splines
with application to the estimation of posterior probabilities;
J. Amer.\ Stat.\ Assoc; X; 19XX; XX;

%Villemoes1994
% larry
\rhl{V}
\refP Villemoes, Lars F.;
Wavelet analysis of refinable functions;
\ChamonixIIb; 493--500;

%Villemoes1994b
% hogan 19nov95
\rhl{V}
\refJ Villemoes, L. F.;
Wavelet analysis of refinement equations;
\SJMA; 25(5); 1994; 1433--1460;

%Villemoes1997
% larry 10sep99
\rhl{V}
\rhl{V}
\refP Villemoes, L. F.;
Nonlinear approximation with Walsh atoms;
\ChamonixIIIb; 329--336;

%Villiers1993
% carl
\rhl{V}
\refJ Villiers,  J. M. de;
A convergence result in nodal spline interpolation;
\JAT; 74(3); 1993; 266--279;
% spline interpolation made local by use of additional knots

%Villiers1993b
% carl
\rhl{V}
\refJ Villiers,  J. M. de;
A nodal spline interpolant for the Gregory rule of even order;
\NM; 66(1); 1993; 123--137;
% quadrature, univariate, local

%VilliersRohwer1987
% larry
\rhl{V}
\refJ Villiers,  J. M. de, Rohwer, C. H.;
Optimal local spline interpolants;
\JCAM; 18; 1987; 107--119;

%VilliersRohwer1989
\rhl{V}
\refR Villiers,  J. M. de, Rohwer, C. H.;
A general order nodal spline generalization of the Lagrange interpolant;
Univ.\ of Stellenbosch, South Africa; 1989;

%VilliersRohwer1991
% author
\rhl{V}
\refP Villiers,  J. M. de, Rohwer, C. H.;
A nodal spline generalization of the Lagrange interpolant;
\Progress; 201--211;

%VilliersRohwer1992
% sonya 05mar08
\rhl{V}
\refR Villiers,  J. M. de, Rohwer, C. H.;
Approximation properties of a nodal spline space;
submitted to \JAT\ but not published; 1992;

%VilliersRohwer1994b
% . 05mar08
\rhl{V}
\refQ Villiers,  J. M. de, Rohwer, C. H.;
Sharp bounds for the Lebesgue constant in quadratic nodal spline interpolation;
(Approximation and Computation: A Festschrift in Honor of Walter Gautschi),
 R. V. M. Zahar (ed.),
ISNM 119, Birkh\"auser Verlag (Basel-Boston-Berlin); 1994; 157--178;

%Vincenti1986a
% shayne 26oct95
\rhl{V}
\refJ Vincenti, G.;
On the computation of the coefficients of $s$-orthogonal polynomials;
\SJNA; 22(6); 1986; 1290--1294;
% numerical computation of the zeros of the monic polynomial of fixed degree
% which has minimum L_p-norm (see also Burgoyne67)

%VinetZhedanov2004
% carl 03apr06
\rhl{}
\refJ Vinet, Luc, Zhedanov, Alexei;
A characterization of classical and semiclassical orthogonal polynomials from
   their dual polynomials;
\JCAM; 172; 2004; 41--48;
% picks up on BoorSaff86 and Borodin02

%Viswanadham1999
\rhl{V}
\refD Viswanadham,  K. N. S. K.;
Finite element method for time dependent problems with B-splines;
Indian Inst.\ of Tech., Bombay; xxx;

%VittitowXX
\rhl{V}
\refR Vittitow,  W. L.;
Interpolation to arbitrarily spaced data;
Thesis; XX;

%Vogelius1983
% author 20jun97
\rhl{V}
\refJ Vogelius, Michael;
A right-inverse for the divergence operator in spaces of piecewise
   polynomials;
\NM; 41; 1983; 19--37;

%Volk1978
% larry
\rhl{V}
\refR Volk, W.;
Die numerische Behandlung Fredholm'scher Integralgleichungen zweiter Art
mittels Splinefunktionen;
Diplomarbeit, Berlin; 1978;

%Volk1980
\rhl{V}
\refR Volk, W.;
Fehlerabsch\"atzungen f\"ur einige Spline-Interpolationsaufgaben;
HMI-B 328; 1980;

%Volk1982
\rhl{V}
\refR Volk, W.;
Spezielle Methoden f\"ur Splinefunktionen zu \"aquidistanten Gittern;
HMI-B 382; 1982;

%Volk1988a
% author 20apr99
\rhl{V}
\refJ Volk, W.;
An efficient raster evaluation method I: univariate polynomials;
\C; 40; 1988; 163--173;

%Volk1988b
% author 20apr99
\rhl{V}
\refQ Volk, W.;
Die Auswertung von Polynomen mehrerer Ver\"anderlicher auf Punktrastern;
(Aktuelle Entwicklungen in der Graphischen
Datenverarbeitung / Austrographics '88), A. Clauer and W. Purgathofer
(eds.), Springer-Verlag (Heidelberg); 1988; 237--251;
% http://user.berlin.de/~wolfgang.volk

%Volk1989
% author 20apr99
\rhl{V}
\refQ Volk,  W.;
Die Auswertung von Splinefunktionen einer Ver\"anderlichen auf Punktrastern;
% Siemens Systemtechnik, Berlin: 1988:
(Proceedings of the 10th Symposium on Algorithms), F. Kluska (ed.),
Vysok\'e Tatry - Strbsk\'e Pleso (???); 1989; 327--330;

%Volk1990
% author 20apr99
\rhl{V}
\refJ Volk, W.;
Making the difference interpolation method for splines more stable;
\JCAM; 33; 1990; 53--59;

%Volk1999a
\rhl{V}
\refR Volk,  W.;
Nonparametric representation of B\'ezier curves;
xxx; xxx;

%Volkov1984a
% author
\rhl{}
\refJ Volkov, Yu. S.;
??? (Russian);
Vychisl.\ Sistemy; 106; 1984; 41--56;

%Volkov1984b
% author
\rhl{}
\refR Volkov, Yu. S.;
Uniform convergence of derivatives of interpolating splines of odd degree;
preprint n.~62, Akad.\ Nauk SSSR, Sibirsk.\ Otd., Inst.\ Mat. (Novosibirsk),
11p; 1984;

%Volkov2005a
% carl 03apr06
\rhl{}
\refJ Volkov, Yu.~S.;
Totally positive matrices in the methods of constructing interpolation
   splines of odd degree;
Siberian Adv.\ in Math.; 15(N4); 2005; 1--30;
% a bound for the condition number of the linear system that arises in the 
% construction of quintic interpolating splines

%Volkov2005b
% carl 03apr06
\rhl{}
\refJ Volkov, Yu.~S.;
Unconditional convergence of one more middle derivative for odd-degree spline
   interpolation;
Doklady Mathematics; 71(2); 2005; 250--252;
% transl from \DAN: 401(1): 2005: 592--594:
% settles the conjecture that, in spline interpolation of order 2n, the induced
% projector on (n-1)st derivatives is bounded independently of the knots.
% Also connects ...

%Voronovskaja1970
% carl
\rhl{V}
\refB Voronovskaja, E. V.;
The Functional Method and its Applications;
Transl.\ Math.\ Monographs, 28, AMS (Providence, RI); 1970;
% basic stuff on extremal polynomials and Hausdorff Moment Problem.

%Vorst2003
% author 23jun03
\rhl{}
\refB Vorst, Henk van der;
Iterative Krylov Methods for Large Linear Systems;
Cambridge University Press (Cambridge); 2003;
% ISBN 0521818281

%Voss2009a
\rhl{V}
\refJ Voss,  A.;
\"Uber Kurvenpaare in R\"aumen;
Sitzungsberichte, Akadamie der Wissenschaften zu M\"unchen;  39;
	  1909; 106;