papers from before 1990 at ftp.cs.wisc.edu/Approx

These files can be obtained by anonymous

from ftp.cs.wisc.edu/Approx. The files are postscript, and are also available as compress(ed) files, as indicated by the subscript .Z, to be uncompress(ed) before using, as well as as (shorter) gzip(ed) files, as indicated by the subscript .gz, to be extracted by gzip -d .
The files are now also available in pdf. For those from before '98, these pdf files might not look very good in an acrobat reader, but will print just fine.
If you have trouble because of file contamination, specify binary as your first command in ftp.
The files are in order of increasing age.

djlr: ps ps.Z ps.gz pdf
On multivariate approximation by integer translates of a basis function
N. Dyn, I.R.H. Jackson, D. Levin and A. Ron
Nov. 1989
has appeared in
Israel Journal of Mathematics {\bf 78} (1992), 95--130.

studia: ps ps.Z ps.gz pdf
A characterization of the approximation order of multivariate spline spaces
A. Ron
November 1989
has appeared in
Studia Mathematica {\bf 98(1)} (1991), 73--90.

quasi: ps ps.Z ps.gz pdf
The exponentials in the span of the multiinteger translates of a compactly supported function: quasiinterpolation and approximation order
Carl de Boor and Amos Ron
November 1989
has appeared in
J. London Math. Soc. (2); 45; 1992; 519--535;

polideal: ps ps.Z ps.gz pdf
Polynomial ideals and multivariate splines
Carl de Boor, Amos Ron
June 1989
has appeared in
(Multivariate Approximation Theory IV, ISNM 90),
C. Chui, W. Schempp, and K. Zeller (eds.),
Birk\-h\"auser Verlag (Basel); 1989; 31--40;

boxtiling: ps ps.Z ps.gz pdf
Carl de Boor, K. H"ollig
Box-spline tilings
May 1989
has appeared in \AMMo; 98; 1991; 793--802;

twopolspaces: ps ps.Z ps.gz pdf
On two polynomial spaces associated with a box spline
Carl de Boor, Nira Dyn \& Amos Ron
April 1989
has appeared in
\PJM; 147; 1991; 249--267;
% (may'99: corrected and updated the references)

newideal: ps ps.Z ps.gz pdf
On polynomial ideals of finite codimension with applications to box spline theory;
Carl de Boor, Amos Ron
December 1988
has appeared in
\JMAA; 158; 1991; 168--193;
% (de.01: corrected (3.8), changed pi to Pi, updated one reference)

discgreen.html
Fundamental solutions for multivariate difference equations;
Carl de Boor, Klaus H\"ollig, Sherman Riemenschneider
1988
has appeared in
\AJM; 111; 1989; 403--415;

multiint: ps ps.Z ps.gz pdf
On multivariate polynomial interpolation
Carl de Boor, Amos Ron
November 1988
has appeared in Constr. Approx.; 6; 1990; 287--302;
% (13nov98: corrected two misprints and changed the symbol for polynomial
% space from \pi to \Pi)

limorg: ps ps.Z ps.gz pdf
The limit at the origin of a smooth function space;
Carl de Boor, Amos Ron
November 1988
has appeared in \TexasVI; 93--96;

cornercut: ps ps.Z ps.gz pdf
Local corner cutting and the smoothness of the limiting curve;
Carl de Boor
November 1988
has appeared in \CAGD; 7; 1990; 389--397;

chebspline: ps ps.Z ps.gz pdf
The exact condition of the B-spline basis may be hard to determine
Carl de Boor
July 1988
has appeared in \JAT; 60; 1990; 344--359;

csd1: ps ps.Z ps.gz pdf
A necessary and sufficient condition for the linear independence of the integer translates of a compactly supported distribution
Amos Ron
1988
has appeared in:
Constructive Approximation {\bf 5}(1989), 297--308.

ebs4: ps ps.Z ps.gz pdf
Local approximation by certain spaces of multivariate exponential-polynomials, approximation order of exponential box splines and related interpolation problems
Nira Dyn and Amos Ron
January 1988
has appeared in:
\TAMS; 319; 1990; 381--403

whatisspline: ps ps.Z ps.gz pdf
What is a multivariate spline?
Carl de Boor
August 1987
has appeared
(Proc.\ First Intern.\ Conf.\ Industr.\ Applied Math., Paris 1987), J.\
McKenna and R. Temam (eds.), SIAM (Philadelphia PA); 1988; 90--101;

bsplloccond: ps ps.Z ps.gz pdf
The condition of the B-spline basis for polynomials
Carl de Boor
April 1987
has appeared as
\SJNA; 25(1); 1988; 148--152;
but the journal's final computer-aided processing messed up the paper through
the omission of various words (that happened to lie beyond column 80 on a
line in the TeX file).

bsplbasic: ps ps.Z ps.gz pdf
B-spline basics
Carl de Boor
MRC 2952, 1986
in (Fundamental Developments of Computer-Aided Geometric Modeling),
Les Piegl (ed.), Academic Press (London) 1993; 27--49;
% Corrected (in Section 12) on 04 mar 96.
% Scaling of figures adjusted and misprints corrected on 03 jun 96
% A misprint corrected (and adjusted to current tex-macros) on 06 jun 96
% A misprint corrected on 12feb98
% A reference updated 27apr09 but the change to (2.4b) made then rescinded on 30mar10

birmingham: ps ps.Z ps.gz pdf
Multivariate Approximation
Carl de Boor
MRC 2950, August 1986
in (State of the Art in Numerical Analysis),
A. Iserles and M. Powell (eds.),
Institute Mathematics Applications (Essex); 1987; 87--109;
% 10mar09: some references, some notation (for pol.spaces, intervals, etc)
% updated; unfortunately, the picture files are lost.

BBform: ps ps.Z ps.gz pdf
$B$--form basics;
Carl de Boor
1986
in (Geometric Modeling: Algorithms and New Trends),
G. E. Farin (ed.),
SIAM Publications (Philadelphia); 1987; 131--148;
% 30nov09 supplied the missing Figure 3, and corrected a typo in (3.3) and in
% last display before Section 6.

polshift: ps ps.Z ps.gz pdf
The polynomials in the linear span of integer translates of a compactly supported function
Carl de Boor
1986
has appeared in: \CA; 3; 1987; 199--208;
% may99: updated the references, corrected various typos, and made the changes:
% \Pi --> \tilde\Pi, \pi -->\Pi, scale-invariant --> dilation-invariant,
% scale (S_h) --> ladder (S_h)

convcardseries.h
Convergence of cardinal series;
Carl de Boor, Klaus H\"ollig, Sherman Riemenschneider
August 1985
has appeared: \PAMS; 98(3); 1986; 457--460;

notaknot: ps ps.Z ps.gz pdf
Convergence of cubic spline interpolation with the not-a-knot condition
Carl de Boor
1985
MRC TSR 2876, October 1985

partitions_of_unity
Partitions of unity and approximation
Carl de Boor and Ronald DeVore
May 1984
has appeared in \PAMS; 93(4); 1985; 705--709;

tpproof
A geometric proof of total positivity for spline interpolation
Carl de Boor and Ron DeVore
March 1984
has appeared in \MC; 45(172); 1985; 497--504;

convbivcard.pdf
Convergence of bivariate cardinal interpolation;
C. de Boor, K. H\"ollig, S. Riemenschneider
1984
has appeared in \CA; 1; 1985; 183--193;

contrapp: ps ps.Z ps.gz pdf
Controlled approximation and a characterization of the local approximation order
Carl de Boor and R.-Q. Jia
1984
has appeared in Proc.\ AMS; 95(4); 1985; 547--553;
http://www.ams.org/journals/proc/1985-095-04/S0002-9939-1985-0810161-X/S0002-9939-1985-0810161-X.pdf

bivcard.pdf
Bivariate cardinal interpolation by splines on a three-direction mesh;
Carl de Boor, Klaus H\"ollig, Sherman Riemenschneider;
1984
\IJM, 29(4), 1985, 533--566;

c1counter
Approximation order from bivariate $C^1$-cubics: A counterexample
Carl de Boor and Klaus H"ollig
1982
has appeared as
\PAMS; 87(4); 1983; 649--655;

approxorder
Approximation order from smooth bivariate splines
C. de Boor, R. DeVore, K. H\"ollig
1982
has appeared in TexasIV; 353--357;

lancaster_lectures.pdf
Topics in multivariate approximation theory
C. de Boor
May 1982
TSR #2379, Mathematics Research Center, University of Wisconsin-Madison

boxsplinestart
Approximation by smooth multivariate splines
Carl de Boor and Ron DeVore
December 1981
has appeared in \TAMS; 276(2); 1983; 775--788;

infsignreg
Inverses of infinite sign regular matrices
C. de Boor, S. Friedland, and A. Pinkus
November 1980
has appeared: \TAMS; 274(1); 1982; 59--68;

multirecur
Recurrence relations for multivariate B-splines
Carl de Boor and Klaus H\"ollig
May 1981
has appeared: \PAMS; 85(3); 1982; 397--400;

inversebiinfband
The inverse of a totally positive bi-infinite band matrix
C. de Boor
November 1980
has appeared: \TAMS; 274(1); 1982; 45--58;

superconvergence
Local piecewise polynomial projection methods for an O.D.E.\ which give high-order convergence at knots
Carl de Boor and Blair Swartz
summer 1980
has appeared in \MC; 36; 1981; 21--33;

maxnormbound: ps ps.Z ps.gz pdf
On a max-norm bound for the least-squares spline approximant
Carl de Boor
1980
has appeared in
(Approximation and Function Spaces),
C. Ciesielski (ed.),
North Holland (Amsterdam); 1981; 163--175;

colloceignumer
Collocation approximation to eigenvalues of an ordinary differential equation: Numerical illustrations;
Carl de Boor and Blair Swartz
March 1980
has appeared in \MC; 36(153); 1981; 1--19;

colloceigprinc
Collocation approximation to eigenvalues of an ordinary differential equation: The principle of the thing;
Carl de Boor and Blair Swartz
March 1979
has appeared in \MC; 35(151); 1980; 679--694;

nwidth
C. de Boor, R. DeVore, K. H\"ollig
Mixed norm $n$-widths
March 1979
has appeared in \PAMS; 80(4); 1980; 577--583;

tensor.pdf
Efficient Computer Manipulation of Tensor Products:
Carl de Boor
oct 1978
has appeared in
ACM Trans. Math. Software; 5(2); 1979; 173--182;
Final production introduced many typos, all marked in the present copy
see Corrigenda, ACM Trans. Math. Software; 5(4); 1979; 525;

agee: ps ps.Z ps.gz pdf
How does Agee's smoothing method work?
Carl de Boor
1978
has appeared in
(Proceedings of the 1979 Army Numerical Analysis and Computers Conference),
xxx (ed.), ARO Rept.\ 79-3, Army Research Office (Triangle Park NC); 1979;
299--302;

Golomb_1978_remastered.pdf
Stability of interpolating elastica;
Michael Golomb
may 1978
has appeared as: MRC TSR #1852;

jacobi.pdf
The Numerically Stable Reconstruction of a Jacobi Matrix from Spectral Data;
Carl de Boor and G. H. Golub
apr 1977
\LAA; 21; 1978; 245--360;

survey76: ps ps.Z ps.gz pdf
Splines as linear combinations of B-splines. A Survey
Carl de Boor
1976
has appeared in \TexasII; 1--47;
% corrected version (with updated references) 19sep97
% left off an extraneous label (6.1) 01aug03

oddbiinf: ps ps.Z ps.gz pdf
Odd-degree spline interpolation at a biinfinite knot sequence
Carl de Boor
\Tex-version of MRC TSR #1666, August 1976
has appeared in \BonnI; 30--53;

l2inlinfconj
A bound on the $L_\infty$-norm of $L_2$-approximation by splines in terms of a global mesh ratio;
Carl de Boor
1975
has appeared:
\MC; 30(136); 1976; 765--771;
http://www.ams.org/journals/mcom/1976-30-136/S0025-5718-1976-0425432-1/S0025-5718-1976-0425432-1.pdf

bsplcalcintegral.pdf
On calculating with B-splines II. Integration;
C. de Boor, T. Lyche, L. L. Schumaker;
1975
(warning: it's a 10Mb file)
in: Numerische Methoden der Approximationstheorie Vol.\ 3, ISNM 30),
L. Collatz, G. Meinardus, and H. Werner (eds.),
Birk\-h\"auser Verlag (Basel); 1976; 123--146;

loclinfl: ps ps.Z ps.gz pdf
On local linear functionals which vanish at all $B$-splines but one;
Carl de Boor
1975
has appeared in (Theory of Approximation with Applications),
A. G. Law and N. B. Sahney (eds.),
Academic Press (New York); 1976; 120--145;

budanfourier: ps ps.Z ps.gz pdf
Cardinal interpolation and spline functions VIII: The Budan Fourier theorem for splines and applications;
Carl de Boor and I. J. Schoenberg
feb 1975
has appeared in (Lecture Notes in Mathematics 501), K. B\"ohmer (ed),
Springer-Verlag (Berlin); 1976; 1--77;
% corrected jul2000 a la KohlerNikolov95a

smallderiv: ps ps.Z ps.gz pdf
A smooth and local interpolant with ``small'' $k$-th derivative;
Carl de Boor
1975
has appeared in
(Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations),
A. Aziz (ed.), Academic Press (New York); 1975;
177--197;

howsmall: ps ps.Z ps.gz pdf
How small can one make the derivatives of an interpolating function?;
Carl de Boor
1973
has appeared as \JAT; 13; 1975; 105--116;
% corrected version (with updated references) 22oct99

cubicnullspline.pdf
On cubic spline functions that vanish at all knots;
Carl de Boor
1973
\AiM, 20(1), 1976, 1--17;

perfect_spline
A remark concerning perfect splines;
Carl de Boor;
1973
has appeared as \BAMS; 80(4); 1974; 724--727;
http://www.ams.org/journals/bull/1974-80-04/S0002-9904-1974-13572-X/S0002-9904-1974-13572-X.pdf

tp.pdf
Total positivity of the spline collocation matrix;
Carl de Boor;
1974
\JMM, 25(6), 1976, 724--727;

splbound: ps ps.Z ps.gz pdf
On bounding spline interpolation;
Carl de Boor
1973
\JAT; 14(3); 1975; 191--203;
% added a footnote pointing out that Jia disproved the conjecture, in %Jia88d

quasiint: ps ps.Z ps.gz pdf
The quasi-interpolant as a tool in elementary polynomial spline theory;
Carl de Boor
1973
has appeared in \TexasI; 269--276;

goodappr: ps ps.Z ps.gz pdf
Good approximation by splines with variable knots;
Carl de Boor
1973
has appeared in \EdmontonI; 57--72;

nonnegcoefs
Carl de Boor and James W. Daniel
Splines with nonnegative $B$-spline coefficients
april 1973
has appeared: \MC; 28(126); 1974; 565--568;

LArep71.pdf
Subroutine Package for Calculating with B-splines;
Carl de Boor
August 1971
report LA-4728-MS Los Alamos scientific laboratory,
An extended version has appeared as
``Package for calculating with B-splines'', \SJNA, 14, 1977, 441--472.

bsplcalc.pdf
On calculating with $B$-splines;
Carl de Boor
september 1970
\JAT; 6; 1972; 50--62;

gamma: ps ps.Z ps.gz pdf
On the approximation by $\gamma$-polynomials;
Carl de Boor
1969
has appeared in \MadisonII; 157--183;

unifappr: ps ps.Z ps.gz pdf
On uniform approximation by splines
Carl de Boor
1967
has appeared as \JAT; 1; 1968; 219--235;
4oct08 various misprints have been corrected

tr20: ps ps.Z ps.gz pdf
Least Squares Cubic Spline Approximation I -- Fixed Knots
Carl de Boor, John R. Rice
CSD TR 20 April 1968

tr21: ps ps.Z ps.gz pdf
Least Squares Cubic Spline Approximation II -- Variable Knots
Carl de Boor, John R. Rice
CSD TR 21 April 1968
% error in NUBAS corrected 3oct01

spaprmom.pdf
On local spline approximation by moments;
Carl de Boor
Sep 1966
has appeared in
\JMM; 17; 1968; 729--735;

deboorphd: ps ps.Z ps.gz pdf
The method of projections as applied to the numerical solution of two point boundary value problems using cubic splines
Carl de Boor Ph.D. thesis, Univ.\ Michigan
August 1966
% corrected version (with updated references) 4apr96

lynch: ps ps.Z ps.gz pdf
On splines and their minimum properties;
Carl de Boor and Robert E. Lynch
1965
has appeared in
\JMM; 15; 1966; 953--969;

bbt.pdf
Nonlinear inrterpolation by splines, pseudosplines and elastica;
Garrett Birkhoff, Hermann Burchard, Donald Thomas;
february 1965
VERY LONG FILE, 4.8Mb
GMR 468, General Motors Research Laboratories (Warren MI); 1965;1

birkhoff_error.pdf
Error bounds for spline interpolation;
Garrett Birkhoff & Carl de Boor;
1964
\JMM, 13(5), 1964, 827--835;

birkhoff.pdf
Piecewise polynomial interpolation and approximation;
Garrett Birkhoff and Carl R. de Boor;
1965
VERY LONG FILE, 8.1Mb
has appeared in
\Generalmotors; 164--190;

baoddspline.pdf
Best approximation properties of spline functions of odd degree;
Carl de Boor;
1963
\JMM, 12(5), 1963, 747--750;

bicubic.pdf
Bicubic spline interpolation;
Carl de Boor
1960
VERY LONG FILE, 4.8Mb
has appeared in
\JMP (J.Mathematics and Physics); 41(3); 1962; 212--218;

viva_vi: ps ps.Z ps.gz pdf
Viva vi!, (a brief introduction to vi)
Carl de Boor
1987
version: 03aug03

intro: ps ps.Z ps.gz pdf
TeXnicalities (an informal introduction to TeX use) (the odd pages)
Carl de Boor
1987
version: 06feb99

ttintro: ps ps.Z ps.gz pdf
TeXnicalities (an informal introduction to TeX use) (the even pages)
Carl de Boor
1987
version: 06feb99

format.tex
A file of plain TeX macros useful for writing papers and books in plain TeX (including automatic sequencing of formal items and items in the bibliography, and the exact placement of items).
Carl de Boor
1983
version: 31may04

message.mm
a self-unwrapping wrapper containing files for simplifying the safe mailing of files via email.
Carl de Boor
1989
version: mar 96

isobib: ps ps.Z ps.gz pdf
List of publications of I. J. Schoenberg
(Carl de Boor)
1987
updated 10mar09