papers on Approximation Order 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.

hangron: ps ps.Z ps.gz pdf
Nonlinear Approximation Using Gaussian Kernels;
Thomas Hangelbroek and Amos Ron
2010
appeared in:
JFA; xx(x); 2010; xxx--xxx;

ard: ps ps.Z ps.gz pdf
Approximation using scattered shifts of a multivariate function;
Ronald DeVore and Amos Ron
feb 2008
TAMS; xx(x); 2010; xxx-xxx;

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

lcamp: ps ps.Z ps.gz pdf
L-CAMP: Extremely local high-performance wavelet representations in high spatial dimension;
Youngmi Hur and Amos Ron
november 2005
IEEE Trans.\ Info.\ Theory, {\bf 54 (5)} (2008), 2196--2209.

pcf: ps ps.Z ps.gz pdf
New constructions of piecewise-constant wavelets;
Youngmi Hur and Amos Ron
may 2005
ETNA, Special Volume on Constructive Function Theory {\bf 25}
(2006), 138--157.

huron: ps ps.Z ps.gz pdf
CAPlets: wavelet representations without wavelets;
Youngmi Hur and Amos Ron
march 2005

olgamos: ps ps.Z ps.gz pdf
Approximation order of shift-invariant subspaces of $W_s^2(R^d)$
Olga Holtz and Amos Ron
May 2004
\JAT; 132; 2005; 97--148;

rbf_err_anal: ps ps.Z ps.gz pdf
An error analysis for radial basis function interpolation
Michael J. Johnson
jan 2003
has appeared
\NM; 98; 2004; 675--694;

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;

dhrs: ps ps.Z ps.gz pdf
Framelets: MRA-based constructions of wavelet frames
Ingrid Daubechies, Bin Han, Amos Ron, Zuowei Shen
feb 2001
\ACHA; 14; 2003; 1--46;

interpolatepsi: ps ps.Z ps.gz pdf
Scattered data interpolation from principal shift-invariant spaces
Michael J. Johnson
feb 2000
\JAT; 113; 2001; 172--188;

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)

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;

BDR4: ps ps.Z ps.gz pdf
Approximation orders of FSI spaces in $L_2(\Rd)$
Carl de Boor, Ron DeVore, and Amos Ron
March 1996
additional references added June-July 1996
referees' comments incorporated Aug/Sep 1996
a minor but useful variation of main result and add'l refs added feb97
An earlier version was, unfortunately, printed as
\CA; 14; 1998; 411--429;
The correct version is
\CA; 14; 1998; 631--652;

perturb: ps ps.Z ps.gz pdf
Approximation in $L_p(\Rd)$ from spaces spanned by the perturbed integer translates of a radial basis function
Michael J. Johnson
May 1995
\JAT; 107(2); 2000; 163--203;

smoothwav: ps ps.Z ps.gz pdf
Smooth refinable functions provide good approximation orders
Amos Ron
February 1995
SIAM J. Math. Anal. {\bf 28} (1997), 731--748.

upbound: ps ps.Z ps.gz pdf
An upper bound on the approximation power of principal shift-invariant spaces
Michael J. Johnson
December 1994
appeared in:
\CA; 13(2); 1997; 155--176;

lowbound: ps ps.Z ps.gz pdf
On the approximation power of principal shift-invariant subspaces of $L_p(R^d)$
Michael J. Johnson
December 1994
\JAT; 91(3); 1997; 279--319;

pscattered: ps ps.Z ps.gz pdf
$L^p$-approximation orders with scattered centres
Martin D. Buhmann and Amos Ron
January 1994
\ChamonixIIb; 93--112;

approxloc: ps ps.Z ps.gz pdf
Approximation orders of and approximation maps from local principal shift-invariant spaces
Amos Ron
May 1993
\JAT; 81(1); 1995; 38--65;

sct1: ps ps.Z ps.gz pdf
Negative observations concerning approximations from spaces generated by scattered shifts of functions vanishing at $\infty$
Amos Ron
September 1992
has appeared in J. Approx. Theory; 78(3); 1994; 364--372;

aowoquasi: ps ps.Z ps.gz pdf
Approximation order without quasi-interpolants
Carl de Boor
August 1992
has appeared in \TexasVII; 1--18;

aoradial: ps ps.Z ps.gz pdf
The $L_2$-Approximation Orders of Principal Shift-Invariant Spaces Generated by a Radial Basis Function
Amos Ron
March 1992
has appeared in \Nmatnion; 245--268;

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;

l2shift: ps ps.Z ps.gz pdf
Approximation from shift-invariant subspaces of $L_2(\RR^d)$
Carl de Boor, Ronald A. DeVore, Amos Ron
July 1991
has appeared in Trans.Amer.Math.Soc. 341; 1994; 787--806;
% note, this file has the name `ell-2-shift', not `one-two-shift'.
% misprint corrected: 19oct94, 17nov97

aoinfty: ps ps.Z ps.gz pdf
Fourier analysis of the approximation power of principal shift-invariant spaces
Carl de Boor, Amos Ron
July 1991
has appeared in Constr.Approx.; 8; 1992; 427--462;

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.

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;

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

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;

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

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;

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

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

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

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

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