papers on multivariate splines 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.

idl16.pdf
Complete graphs: the space of simplicial cones, and their path tree representation;
Amos Ron & Shengnan (Sarah) Wang
august 2017

idl13.pdf
Bivariate truncated powers: complete intersection decompositions and the spline representation;
Amos Ron & Shengnan (Sarah) Wang
june 2017

idl12.pdf
Truncated power splines: acyclic resolutions of cone polynomials;
Amos Ron & Shengnan (Sarah) Wang
june 2017

TPS_val.pdf
The role of inner summaries in the fast evaluation of thin-plate splines;
Michael J. Johnson
november 2011
has appeared:
\AiCM; 39(1); 2013; 1--25;

TPS_val.tar.gz
Matlab and C programs for the fast evaluation of thin-plate splines;
Michael J. Johnson
november 2011
\AiCM; 39(1); 2013; 1--25;

dahmen: ps ps.Z ps.gz pdf
The way things were in multivariate splines: A personal view;
Carl de Boor
april 2009
in Multiscale, Nonlinear and Adaptive Approximation, R. DeVore and A. Kunoth
(eds.), Springer Verlag (Berlin-Heidelberg, Germany); 2009; 19--37;

boxsubdv: ps ps.Z ps.gz pdf
Box splines revisited: convergence and acceleration methods for the subdivision and the cascade algorithms;
Carl de Boor and Amos Ron
december 2006
\JAT; 150(1); 2008; 1--23;

TPSerror: ps ps.Z ps.gz pdf
Error estimates for thin plate spline approximation in the disc;
Thomas Hangelbroek
december 2006

unstable.pdf
A note on the limited stability of surface spline interpolation;
Michael Johnson
2005
has appeared
\JAT; 141(2); 2006; 182--188;

Lp_order_SSI: ps ps.Z ps.gz pdf
The $L_p$ approximation order of surface spline interpolation for $1\le p \le 2$
Michael J. Johnson
apr 2002
\CA; 20(2); 2004; 133--167;

ssiorder: ps ps.Z ps.gz pdf
The $L_2$-approximation order of surface spline interpolation
Michael J. Johnson
jun 1999
Math. Comp. 70, 719--737 (2001)

compact: ps ps.Z ps.gz pdf
On the error in surface spline interpolation of a compactly supported function
Michael J. Johnson
sep 1998, dec 1998
Kuwait J. Sci. Eng. 28, 37--54 (2001)

overcome: ps ps.Z ps.gz pdf
Overcoming the boundary effects in surface spline interpolation
Michael J. Johnson
nov 1998
IMA J. Numer. Anal. 20, 405--422 (2000)

improved: ps ps.Z ps.gz pdf
An improved order of approximation for thin-plate spline interpolation in the unit disc
Michael Johnson
February 1998
has appeared in
\NM; 84(3); 2000; 451--474;

surfspli: ps ps.Z ps.gz pdf
A bound on the approximation order of surface splines
Michael Johnson
October 1997
\CA; 14; 1998; 429--438;

multpp: ps ps.Z ps.gz pdf
Multivariate piecewise polynomials,
Carl de Boor
October 1992
has appeared in Acta Numerica; 2; 1993; 65--109;

aobivar: ps ps.Z ps.gz pdf
A sharp upper bound on the approximation order of smooth bivariate pp functions
Carl de Boor and Rong-Qing Jia
March 1992
has appeared in J.Approx.Theory; 72(1); 1993; 24--33;

quasiaprx: ps ps.Z ps.gz pdf
Quasiinterpolants and approximation power of multivariate splines
Carl de Boor
July 1990
has appeared in
(Computations of curves and surfaces), Dahmen, Gasca, Micchelli
(eds.), Kluwer (Dordrecht, Netherlands); 1990; 313--345;

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.

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;

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;

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.

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

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

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;

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;

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

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;

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;

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;