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Content of the read.me file at ftp.cs.wisc.edu/Approx
Content of the read.me file at ftp.cs.wisc.edu/Approx
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These are the files that 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.
If you have trouble because of file contamination, specify binary
as your
first command in ftp.
The files are in order of increasing age.
bmr.ps,
bmr.ps.Z :=
Asymptotically Optimal Approximation and Numerical Solutions of Differential
Equations
Martin D. Buhmann, Charles A. Micchelli, Amos Ron}
October 1996
cg.ps,
cg.ps.Z :=
Tight compactly supported wavelet frames of arbitrarily high smoothness
Karlheinz Gr\"ochenig, Amos Ron
September 1996
BDR4.ps,
BDR4.ps.Z :=
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
to appear in \CA
tight.ps,
tight.ps.Z :=
Compactly supported tight affine spline frames in $L_2(\Rd)$
Amos Ron and Zuowei Shen
February 1996
to appear in Math. Comp.
multiw.ps,
multiw.ps.Z :=
Stability and independence of the shifts of finitely many refinable
functions
Thomas A. Hogan
January 1996
affine.ps,
affine.ps.Z :=
Affine systems in $L_2(\Rd)$: the analysis of the analysis operator
Amos Ron, Zuowei Shen
December 1995
zerocount.ps,
zerocount.ps.Z :=
The multiplicity of a spline zero
Carl de Boor
December 1995/ January 96 (reflect referee's comments)
to appear in Ann. Numer.Math.
ker2.ps,
ker2.ps.Z :=
On ascertaining inductively the dimension of the joint kernel
of certain commuting linear operators. II
Carl de Boor, Amos Ron, Zuowei Shen
May 1995
to appear in Adv. in Math.
cdr.ps,
cdr.ps.Z :=
How smooth is the smoothest function in a given refinable space?
Albert Cohen, Ingrid Daubechies, Amos Ron
May 1995
to appear in Applied and Computational Harmonic Analysis
perturb.ps,
perturb.ps.Z :=
Approximation in $L_p(\Rd)$ from spaces spanned by the perturbed integer
translates of a radial basis function
Michael J. Johnson
May 1995
sauerxu.ps,
sauerxu.ps.Z :=
On the Sauer-Xu formula for the error in multivariate polynomial interpolation;
Carl de Boor
March 1995
to appear in Math.Comp.
frame2.ps,
frame2.ps.Z :=
Gramian analysis of affine bases and affine frames
Amos Ron and Zuowei Shen
March 1995
\TexasVIIIw; 375--382;
multdvdf.ps,
multdvdf.ps.Z :=
A multivariate divided difference
Carl de Boor
March 1995
\TexasVIIIa; 87--96;
smoothwav.ps,
smoothwav.ps.Z :=
Smooth refinable functions provide good approximation orders
Amos Ron
February 1995
to appear in SIAM J. Math. Anal.
stabindep_texasviii.ps,
stabindep_texasviii.ps.Z :=
Stability and independence of the shifts of a multivariate refinable function
Tom Hogan
February 1995
\TexasVIIIw; 159--166;
stabindep.ps,
stabindep.ps.Z :=
Stability and independence of the shifts of a multivariate refinable function
Tom Hogan
February 1995
upbound.ps,
upbound.ps.Z :=
An upper bound on the approximation power of principal shift-invariant spaces
Michael J. Johnson
December 1994
Constructive Approximation, to appear
lowbound.ps,
lowbound.ps.Z :=
On the approximation power of principal shift-invariant subspaces of $L_p(R^d)$
Michael J. Johnson
December 1994
wh.ps,
wh.ps.Z :=
Weyl-Heisenberg frames and Riesz bases in $L_2(\Rd)$
Amos Ron and Zuowei Shen
October 1994
to appear in Duke Math. J.
symmetries.ps,
symmetries.ps.Z :=
Symmetries of linear functionals
Shayne Waldron
October 1994
hardy.ps,
hardy.ps.Z :=
A multivariate form of Hardy's inequality and $L_p$-error bounds for
multivariate Lagrange interpolation schemes
Shayne Waldron
August 1994
lift.ps,
lift.ps.Z :=
Integral error formul{\ae} for the scale of mean value interpolations which
includes Kergin and Hakopian interpolation
Shayne Waldron
July 1994
hermite.ps,
hermite.ps.Z :=
$L_p$-error bounds for Hermite interpolation and the associated Wirtinger
inequalities
Shayne Waldron
May 1994
extremising.ps,
extremising.ps.Z :=
Extremising the $L_p$-norm of a monic polynomial with roots in a given
interval and Hermite interpolation
Shayne Waldron
May 1994
polintelim.ps,
polintelim.ps.Z :=
Gauss elimination by segments and multivariate polynomial interpolation
Carl de Boor
March 1994
in (Approximation and Computation), R.V.M. Zahar (ed.),
ISNM 119, Birkh\"auser Verlag (Basel-Boston-Berlin); 1994; 1--22;
sphere.ps,
sphere.ps.Z :=
Strictly positive definite functions on spheres
Amos Ron and Xingping Sun
February 1994
to appear in Math. Comp.
frame1.ps,
frame1.ps.Z :=
Frames and stable bases for shift-invariant subspaces of $L_2(\Rd)$
Amos Ron and Zuowei Shen
February 1994
Canad. Math. J. (1995)
pscattered.ps,
pscattered.ps.Z :=
$L^p$-approximation orders with scattered centres
Martin D. Buhmann and Amos Ron
January 1994
scattered.ps,
scattered.ps.Z :=
Radial basis function approximation: from gridded centers to scattered centers
Nira Dyn and Amos Ron
November 1993
Proc. London Math. Soc. (1995)
approxloc.ps,
approxloc.ps.Z :=
Approximation orders of and approximation maps from local principal
shift-invariant spaces
Amos Ron
May 1993
JAT (1995)
boxeval.ps,
boxeval.ps.Z :=
On the evaluation of box splines,
Carl de Boor
March 1993
has appeared in Numer.Algorithms; 5; 1993; 5--23;
multpp.ps,
multpp.ps.Z :=
Multivariate piecewise polynomials,
Carl de Boor
October 1992
has appeared in Acta Numerica; 2; 1993; 65--109;
wav2.ps,
wav2.ps.Z :=
Multiresolution analysis by infinitely differentiable compactly
supported functions
Nira Dyn, Amos Ron
September 1992
ACHA (1995)
stablemask.ps,
stablemask.ps.Z :=
Characterizations of linear independence and stability of the shifts of a
univariate refinable function in terms of its refinement mask
Amos Ron
September 1992
sct1.ps,
sct1.ps.Z :=
Negative observations concerning approximations from spaces generated by
scattered shifts of functions vanishing at $\infty$
Amos Ron
September 1992
has appeared in \JAT; 78(3); 1994; 364--372;
aowoquasi.ps,
aowoquasi.ps.Z :=
Approximation order without quasi-interpolants
Carl de Boor
August 1992
has appeared in \TexasVII; 1--18;
ker.ps,
ker.ps.Z :=
On ascertaining inductively the dimension of the joint kernel
of certain commuting linear operators
Carl de Boor, Amos Ron, Zuowei Shen
June 1992; updated Apr 96 to reflect copy editor's changes
has appeared in \AiAM; 17; 1996; 209--250;
aoradial.ps,
aoradial.ps.Z :=
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,
aobivar.ps.Z :=
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;
wavelet.ps,
wavelet.ps.Z :=
On the construction of multivariate (pre)wavelets
Carl de Boor, Ronald A. DeVore, Amos Ron
February 1992
has appeared in Constr.Approx.; 9; 1993; 123--166;
several.ps,
several.ps.Z :=
The structure of finitely generated shift-invariant spaces in $L_2(\RR^d)$
Carl de Boor, Ronald A. DeVore, Amos Ron
February 1992
has appeared in J. of Functional Analysis 119(1); 1994; 37--78;
polinterr.ps,
polinterr.ps.Z :=
On the error in multivariate polynomial interpolation
Carl de Boor
has appeared in Applied Numerical Mathematics; 10; 1992; 297--305;
l2shift.ps,
l2shift.ps.Z :=
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'.
aoinfty.ps,
aoinfty.ps.Z :=
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,
quasiaprx.ps.Z :=
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;
leastsol.ps,
leastsol.ps.Z :=
The least solution for the polynomial interpolation problem;
Carl de Boor, Amos Ron
has appeared in Math.Zeitschrift; 210; 1992; 347--378;
compleast.ps,
compleast.ps.Z :=
Computational aspects of polynomial interpolation in several variables
Carl de Boor, Amos Ron
has appeared in Math.Comp.; 58; 1992; 705--727;
polintconte.ps,
polintconte.ps.Z :=
Polynomial interpolation in several variables
Carl de Boor
March 1990
has appeared in
(Studies in Computer Science {(in Honor of Samuel D. Conte)}),
R. DeMillo and J. R. Rice (eds.), Plenum Press (New York); 1994; 87--119;
polideal.ps,
polideal.ps.Z :=
Polynomial ideals and multivariate splines;
Carl de Boor, Amos Ron
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;
multiint.ps,
multiint.ps.Z :=
On multivariate polynomial interpolation;
Carl de Boor, Amos Ron
has appeared in Constr. Approx.; 6; 1990; 287--302;
bsplbasic.ps,
bsplbasic.ps.Z :=
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
quasi.ps,
quasi.ps.Z :=
The exponentials in the span of the multiinteger
translates of a compactly supported function:
quasiinterpolation and approximation order
1989
Carl de Boor and Amos Ron
has appeared in
J. London Math. Soc. (2); 45; 1992; 519--535;
BBform.ps,
BBform.ps.Z :=
$B$--form basics;
Carl de Boor
in (Geometric Modeling: Algorithms and New Trends),
G. E. Farin (ed.),
SIAM Publications (Philadelphia); 1987; 131--148;
notaknot.ps,
notaknot.ps.Z :=
Convergence of cubic spline interpolation with the not-a-knot condition
Carl de Boor
MRC TSR 2876, October 1985
contrapp.ps,
contrapp.ps.Z :=
Controlled approximation and a characterization of the local
approximation order;
Carl de Boor and R.-Q. Jia
has appeared in Proc.\ AMS; 95(4); 1985; 547--553;
agee.ps,
agee.ps.Z :=
How does Agee's smoothing method work?
Carl de Boor
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;
survey76.ps,
survey76.ps.Z :=
Splines as linear combinations of B-splines. A Survey
(corrected version (with updated references))
Carl de Boor
has appeared in \TexasII; 1--47;
loclinfl.ps,
loclinfl.ps.Z :=
On local linear functionals which vanish at all $B$-splines but one;
Carl de Boor
has appeared in (Theory of Approximation with Applications),
A. G. Law and N. B. Sahney (eds.),
Academic Press (New York); 1976; 120--145;
quasiint.ps,
quasiint.ps.Z :=
The quasi-interpolant as a tool in elementary polynomial spline theory;
Carl de Boor, 1973
has appeared in \TexasI; 269--276;
tr21.ps,
tr21.ps.Z :=
Least Squares Cubic Spline Approximation II -- Variable Knots
Carl de Boor, John R. Rice
April 1968 CSD TR 21
tr20.ps,
tr20.ps.Z :=
Least Squares Cubic Spline Approximation I -- Fixed Knots
Carl de Boor, John R. Rice
April 1968 CSD TR 20
deboorphd.ps,
deboorphd.ps.Z :=
The method of projections as applied to the numerical solution of two point
boundary value problems using cubic splines
(corrected version (with updated references))
Carl de Boor Ph.D. thesis, Univ.\ Michigan
August 1966
viva_vi.ps,
viva_vi.ps.Z :=
Viva vi!, (a brief introduction to vi)
Carl de Boor
version: aug 96
format.tex,
format.tex.Z :=
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
version: 15 apr 96
verbatim.tex,
verbatim.tex.Z :=
A file of plain TeX macros useful for handling the typesetting of programs
and program-related material in plain TeX.
Carl de Boor
version: 22 se 94
journal.tex,
journal.tex.Z :=
TeX macros of use with the spline bibliography.
Carl de Boor
version: 15 apr 96
proceed.tex,
proceed.tex.Z :=
TeX macros of use with the spline bibliography.
Carl de Boor
version: 19 apr 96
refmac.tex,
refmac.tex.Z :=
TeX macros of use with the spline bibliography.
Carl de Boor
message.mm,
message.mm.Z :=
a self-unwrapping wrapper containing files for simplifying the safe mailing of
files via email.
Carl de Boor
version: mar 96