IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII AAA_readme IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII
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The files for mathematical papers are postscript and pdf, and the former
are also available as
compress(ed) files, as indicated by the subscript .Z, to be uncompress(ed)
before using. Some are also available as gzip(ed) files, as indicated by the
subscript .gz, to be unzipped by the command gzip -d .
If you have trouble because of file contamination, specify binary as your
first command in ftp .
Each item in this list should be in the following format:
, , ..., , < >:=
<author(s)>
<date> (ending in the last two digits of the year)
(further lines are optional)
with the first 4 items each on just one line (including the title). Further,
each <id> is chosen from the following list (taken from update.ftpreadme)
al 'polynomial ideals, commutative algebra and AT'
ao 'Approximation Order'
bs '(exponential and other) box splines'
di 'dimension of kernels of linear operators'
fr 'frames'
la 'linear algebra'
ms 'multivariate splines'
na 'numerical analysis'
ns 'nonlinear splines'
pi 'multivariate polynomial interpolation'
qi 'quasi-interpolation'
rb 'radial basis function approximations'
rf 'refinable functions'
sd 'scattered data approximation'
si 'shift-invariant spaces'
su 'subdivision'
sr 'surveys'
us 'univariate splines'
wv 'wavelets'
WH 'Weyl-Heisenberg systems'
TeX '\Tex, splinebib, file-mailing ...'
These are used to generate the topic-specific webpages.
If <filename> terminates in .ps, links to .ps, ps.Z, ps.gz, and pdf versions
of the file are created.
Further, <link> is required only if <filename> terminates in .html .
For filenames with any other extension, only a link to that file is created.
Here is the list:
us, ns, Elastic_Splines_II.pdf :=
Elastic Splines II: Unicity of optimal s-curves and G2 regularity of splines;
Albert Borb\'ely & Michael J. Johnson;
december 2016
us, ns, Constructive_Framework.pdf :=
A constructive framework for minimal energy planar curves;
Michael J. Johnson & Hakim S. Johnson;
december 2016
\AMC (Applied Mathematics and Computation); 276; 2016; 172--181;
us, ns, elastic_splines_I.pdf :=
Elastic splines I: Existence;
Albert Borb\'ely & Michael J. Johnson;
january 2014
has appeared:
\CA; 40; 2914; 189--218;
ms, rb, sd, na, 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;
ms, rb, sd, na, 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;
us, Bspline_rbf.pdf :=
Minimal degree univariate piecewise polynomials with prescribed Sobolev regularity;
Amal Al-Rashdan, Michael J. Johnson
october 2011
\JAT; 164(1); 2012; 1--5;
rb, Lspline_rbf.pdf :=
Compactly supported piecewise polyharmonic radial functions with prescribed regularity;
Michael J. Johnson
october 2011
\CA 35(2); 2012; 201--223;
us, la, re_shadrin.ps :=
On the (bi)infinite case of Shadrin's theorem concerning the $L_\infty$-boundedness of the $L_2$-spline projector;
Carl de Boor
july 2011
has appeared in the Subbotin 75th anniversary volume
Trudy Instituta Matematiki i Mekhaniki UrO RAN; 17(3); 2011, 25--29;
pi, al, sd stahl.ps :=
On Radon's recipe for choosing correct sites for multivariate polynomial interpolation;
Dominik Stahl and Carl de Boor
june 2011
\JAT; 163(12); 2011; 1854--1858;
al, bs, di, pi, liron.ps :=
External zonotopal algebra;
Nan Li and Amos Ron
april 2011
rb, sb, ao, hangron.ps :=
Nonlinear Approximation Using Gaussian Kernels;
Thomas Hangelbroek and Amos Ron
2010
appeared in:
JFA; xx(x); 2010; xxx--xxx;
al, bs, di, pi, hrx.ps :=
Hierarchical zonotopal spaces;
Olga Holtz, Zhiqiang Xu and Amos Ron
october 2009
to appear in
TAMS; xx(x); 201x; xxx-xxx;
ms, pi, sr, dahmen.ps :=
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;
rb, sd, na, sym_col_fast.pdf :=
A symmetric collocation method with fast evaluation;
Michael Johnson
2008
appeared in
IMAJNA; 29(3); 2009; 773--789;
sd, na, wv, scattered_data_wavelets.pdf :=
Scattered data reconstruction by regularization in B-spline and associated wavelet spaces;
Michael Johnson, Zuowei Shen, Yugong XU
2008
appeared in
\JAT; 159(2); 2009; 197--223;
pi, angpl.ps :=
Multivariate polynomial interpolation: Aitken-Neville sets and generalized principal lattices;
Carl de Boor
april 2008
updated 1may08, 8jul08, 10aug08
\JAT; 161(1); 2009; 411--420;
ao, qi, rb, sd, ard.ps :=
Approximation using scattered shifts of a multivariate function;
Ronald DeVore and Amos Ron
feb 2008
TAMS; xx(x); 2010; xxx-xxx;
al, pi, la, shekht.ps :=
On the pointwise limits of bivariate Lagrange projectors;
Carl de Boor and Boris Shekhtman
november 2007
\LAA; 429(1); 2008; 311--325;
al, bs, di, pi, la, zonotopes.ps :=
Zonotopal algebra;
Olga Holtz and Amos Ron
september 2007
bs, ms, rf, si, su, boxsubdv.ps :=
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;
rb, ms, sd, TPSerror.ps :=
Error estimates for thin plate spline approximation in the disc;
Thomas Hangelbroek
december 2006
fr, wv, WH, apframes.ps :=
Time frequency representations of almost-periodic functions;
Yeon Hyang Kim and Amos Ron
decenber 2006
\CA; xx; 2008; xxx--xxx;
pi, gcn.ps :=
Multivariate polynomial interpolation: conjectures concerning GC-sets;
Carl de Boor
september 2006
proc. 1st Dolomites Workshop: 2006:
07dec06 update
\NA; 45; 2007; 113--125;
ao, rb, sd, ms, unstable.pdf :=
A note on the limited stability of surface spline interpolation;
Michael Johnson
2005
has appeared
\JAT; 141(2); 2006; 182--188;
pi, al, laglimit.ps :=
What are the limits of Lagrange projectors?
Carl de Boor
december 2005
(Constructive Theory of Functions, Varna 2005), B. Bojanov (ed.),
Marin Drinov Acad.\ Publ.\ House (Sofia); 2006; 51--63;
fr, wv, ao, lcamp.ps :=
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.
fr, wv, ao, pcf.ps :=
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.
fr, wv, ao, huron.ps :=
CAPlets: wavelet representations without wavelets;
Youngmi Hur and Amos Ron
march 2005
pi, al, MvsD.ps :=
Ideal interpolation: Mourrain's condition vs $D$-invariance;
Carl de Boor
jan 2005
(Banach Center Publications Vol.~72: Approximation and Probability),
Tadeusz Figiel and Anna Kamont (eds.), IMPAN (Warszawa, Poland); 2006; 49--55;
pi, na, al, texasxi.ps :=
Ideal interpolation;
Carl de Boor
dec 2004
\TexasXI; 59--91;
dec05: three footnotes added
na, dvdsurvey.ps :=
Divided differences;
Carl de Boor
nov 2004
Surveys in Approximation Theory; 1; 2005; 46--69;
http://www.math.technion.ac.il/sat/papers/2
pi, monomint.ps :=
Interpolation from spaces spanned by monomials
Carl de Boor
aug 2004
\AiCM; 26(1-3); 2007; 63--70;
na, efficdvd.ps :=
An efficient definition of the divided difference
Carl de Boor
aug 2004
in (Approximation Theory: A Volume Dedicated to Borislav Bojanov),
D. K. Dimitrov, G. Nikolov, and R. Uluchev (eds.), Marin Drinov Academic
Publ. House (Sofia); 2004; 58--63;
ao, rf, si, olgamos.ps :=
Approximation order of shift-invariant subspaces of $W_s^2(R^d)$
Olga Holtz and Amos Ron
May 2004
\JAT; 132; 2005; 97--148;
pi, rb, radpol.ps :=
On interpolation by radial polynomials
Carl de Boor
dec 2003
as of 21jul04/23feb04
\AiCM; 24; 2006; 143--153;
us, asympterr.ps :=
An asymptotic expansion for the error in a linear map that reproduces polynomials of a certain order
Carl de Boor
apr 2003
\JAT; 134; 2005; 171--174;
us, chakpop.ps :=
The B-spline recurrence relations of Chakalov and of Popoviciu
Carl de Boor and Allan Pinkus
mar 2003
\JAT; 124(1); 2003; 115--123;
fr, si, wv, gsi.ps :=
Generalized shift-invariant systems
Amos Ron and Zuowei Shen
jan 2003
\CA; 22; 2005; 1--45;
ao, rb, sd, rbf_err_anal.ps :=
An error analysis for radial basis function interpolation
Michael J. Johnson
jan 2003
has appeared
\NM; 98; 2004; 675--694;
na, floater.ps :=
A divided difference expansion of a divided difference
Carl de Boor
nov 2002
\JAT; 122(1); 2003; 10--12;
na, pi, leibniz.ps :=
A Leibniz formula for multivariate divided differences
Carl de Boor
apr 2002
\SJNA; 41(3); 2003; 856--868;
ao, ms, rb, sd, Lp_order_SSI.ps :=
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;
si, wv, fr, rf, dim1.ps :=
The Wavelet Dimension Function is The Trace Function of A Shift-Invariant System
Amos Ron, Zuowei Shen
jun 2001
\PAMS; 131(5); 2003;1385--1398;
si, ao, rf, wv, fr, dhrs.ps :=
Framelets: MRA-based constructions of wavelet frames
Ingrid Daubechies, Bin Han, Amos Ron, Zuowei Shen
feb 2001
\ACHA; 14; 2003; 1--46;
us, sr, cagdhand.ps :=
Spline Basics
Carl de Boor
dec 2000
Chapter 6 in \Cagdhand; see (cagd.snu.ac.kr/main.html)
la, us, inverse_basis.ps :=
What is the inverse of a basis?
Carl de Boor
sep 2000
BIT; 41(5); 2001; 880--890;
(the printed version contains a random 7 right in the middle of (4.2), the most
important formula of the paper, and an extra p in the first display on page 889)
si, rb, ao, sd, interpolatepsi.ps :=
Scattered data interpolation from principal shift-invariant spaces
Michael J. Johnson
feb 2000
\JAT; 113; 2001; 172--188;
sr, SIsurvey.ps :=
Introduction to Shift-Invariant Spaces I: Linear Independence
Amos Ron
dec 1999
to appear in
(Multivariate Approximation and Applications),
A. Pinkus, D. Leviatan, N. Dyn, and D. Levin (eds.),
Cambridge University Press (Cambridge); 200x; xxx--xxx;
rf, rst.ps :=
Computing the Sobolev regularity of refinable functions by the Arnoldi Method
Amos Ron, Zuowei Shen, Kim-Chuan Toh
oct 1999
\SJMAA; 23; 2001; 57--76;
pi, polintflats.ps :=
Polynomial interpolation to data on flats in $\Rd$
Carl de Boor, Nira Dyn, Amos Ron
aug 1999
\JAT; 105; 2000; 313--343;
us, mixed.ps :=
On mixed interpolating-smoothing splines and the $\nu$-spline
Scott Kersey
jun 1999
ao, ms, ssiorder.ps :=
The $L_2$-approximation order of surface spline interpolation
Michael J. Johnson
jun 1999
Math. Comp. 70, 719--737 (2001)
la, jordannf.ps :=
On Ptak's derivation of the Jordan normal form;
Carl de Boor
may 1999
\LAA; 310; 2000; 9--10;
us, exists.ps :=
Best near-interpolation by curves: existence and convergence
Scott Kersey
apr 1999
us, optimality.ps :=
Best near-interpolation by curves: optimality conditions
Scott Kersey
apr 1999
pi, mp.ps :=
Computational aspects of multivariate polynomial interpolation: Indexing the coefficients
Carl de Boor
jan/feb 1999
may99 incorporated referee's comments
\AiCM; 12; 2000; 289--301;
rb, ms, compact.ps :=
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)
rb, ms, overcome.ps :=
Overcoming the boundary effects in surface spline interpolation
Michael J. Johnson
nov 1998
IMA J. Numer. Anal. 20, 405--422 (2000)
us, smooth.ps :=
Calculation of the smoothing spline with weighted roughness measure
Carl de Boor
sep 1998
Math.\ Models Methods Appl.\ Sci.; 11(1); 2001; 33--41;
la, na, pi, sr, encoan.ps :=
Multivariate Hermite interpolation (talk at Guernavaca, 13apr99)
Carl de Boor
apr 1999
updated 08feb01 to conform to present-day notation
updated 20apr08 to correct some misprints
sr, wv, texas9.ps :=
Wavelets and their associated operators
Amos Ron
July 1998
\TexasIXc; 283--317;
rf ger.ps :=
A new factorization technique of the matrix mask of univariate refinable functions
Gerlind Plonka and Amos Ron
June 1998
has appeared in \NM; 87(3); 2001; 555--595;
rf, hoganjia.ps :=
Dependency relations among th shifts of a multivariate refinable distribution
Thomas A. Hogan and Rong-Qing Jia
March 1998
to appear in CA
rf, nec_note.ps :=
A note on matrix refinement equations
Thomas A. Hogan
February 1998
\SJMA; 29; 1998; 849--854
ao,ms, rb, improved.ps :=
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;
rf, hardinhogan.ps :=
Refinable subspaces of a refinable space
Douglas P. Hardin and Thomas A. Hogan
February 1998
to appear in PAMS
fr, hk.ps :=
Construction of Compactly Supported Affine Frames in $L_2(\Rd)$
Amos Ron and Zuowei Shen
December 1997
in
(Advances in Wavelets), K. S. Lau (ed.), Springer-Verlag (New York); 1998;
27--50;
ao, rb, ms, surfspli.ps :=
A bound on the approximation order of surface splines
Michael Johnson
October 1997
\CA; 14; 1998; 429--438;
TeX, pi, message.mp5 :=
A selfunwrapping wrapper containing MATLAB 5 programs for the construction and evaluation of the least interpolant to data in any number of dimensions
Carl de Boor
as of February 1999
fr, dframe.ps :=
Affine system in $L_2(\Rd)$ II: dual systems
Amos Ron and Zuowei Shen
July 1997
Appeared in:
J. Fourier Analysis and Appl., Special Issue on Frames {\bf 3} (1997), 617-637.
rf, reg.ps :=
The Sobolev regularity of refinable functions
Amos Ron and Zuowei Shen
March 1997
J. Approx. Theory, {\bf 106(2)} (2000), 185--225.
pi, chamonix.ps :=
The error in polynomial tensor-product, and in Chung-Yao, interpolation
Carl de Boor
February 1997
in
Surface Fitting and Multiresolution Methods
A. Le M\'ehaut\'e, C. Rabut, and L. L. Schumaker (eds),
Vanderbilt University Press (Nashville TN), 35--50.
6apr09: added missing reference to Waldron'98a
us, splerr.ps :=
On the Meir/Sharma/Hall/Meyer analysis of the spline interpolation error
Carl de Boor
December 1996
Appeared in:
\Powellfest; 47--58;
na, bmr.ps :=
Asymptotically Optimal Approximation and Numerical Solutions of Differential Equations
Martin D. Buhmann, Charles A. Micchelli, Amos Ron
October 1996
\Powellfest; 59--82;
fr, cg.ps :=
Tight compactly supported wavelet frames of arbitrarily high smoothness
Karlheinz Gr\"ochenig, Amos Ron
September 1996
\PAMS; 126; 1998; 1101--1107;
ao, si, BDR4.ps :=
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;
fr, tight.ps :=
Compactly supported tight affine spline frames in $L_2(\Rd)$
Amos Ron and Zuowei Shen
February 1996
\MC; 65(216); 1998; 1513--1530;
rf, multiw.ps :=
Stability and independence of the shifts of finitely many refinable functions
Thomas A. Hogan
January 1996
revised February 1997
\JFAA; 3; 1997; 757--774;
fr, affine.ps :=
Affine systems in $L_2(\Rd)$: the analysis of the analysis operator
Amos Ron, Zuowei Shen
December 1995
J. Functional Analysis {\bf 148} (1997), 408-447
us, zerocount.ps :=
The multiplicity of a spline zero
Carl de Boor
December 1995
January 96 (reflect referee's comments)
appeared in
\AoNM; 4; 1997; 229--238;
na, bennett.ps :=
On determining the foot of the continental slope
Carl de Boor
November 1995
revised feb'96
di, ker2.ps :=
On ascertaining inductively the dimension of the joint kernel of certain commuting linear operators. II
Carl de Boor, Amos Ron, Zuowei Shen
May 1995
Adv. in Math. {\bf 123} (1996), 223--242.
rf, cdr.ps :=
How smooth is the smoothest function in a given refinable space?
Albert Cohen, Ingrid Daubechies, Amos Ron
May 1995
Applied and Computational Harmonic Analysis {\bf 3} (1996), 87--89.
ao, rb, perturb.ps :=
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;
na, pi, sauerxu.html := http://www.ams.org/journals/mcom/1996-65-215/S0025-5718-96-00727-2/S0025-5718-96-00727-2.pdf
On the Sauer-Xu formula for the error in multivariate polynomial interpolation;
Carl de Boor
March 1995
\MC; 65; 1996; 1231--1234;
fr, frame2.ps :=
Gramian analysis of affine bases and affine frames
Amos Ron and Zuowei Shen
March 1995
\TexasVIIIw; 375--382;
na, pi, multdvdf.ps :=
A multivariate divided difference
Carl de Boor
March 1995
\TexasVIIIa; 87--96;
% 25mar02: supplied missing g in (4.1) and completed refs [17] and [18].
ao, rf, smoothwav.ps :=
Smooth refinable functions provide good approximation orders
Amos Ron
February 1995
SIAM J. Math. Anal. {\bf 28} (1997), 731--748.
rf, stabindep_texasviii.ps :=
Stability and independence of the shifts of a multivariate refinable function
Thomas A. Hogan
February 1995
\TexasVIIIw; 159--166;
rf, stabindep.ps :=
Stability and independence for multivariate refinable distributions
Thomas A. Hogan
February 1995
revised August 1997
appeared in
\JAT; 98(2); 1999; 248--270;
ao, si, upbound.ps :=
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;
ao, si, lowbound.ps :=
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;
WH, wh.ps :=
Weyl-Heisenberg frames and Riesz bases in $L_2(\Rd)$
Amos Ron and Zuowei Shen
October 1994
Duke Math. J. {\bf 89} (1997), 237-282.
na, symmetries.ps :=
Symmetries of linear functionals
Shayne Waldron
October 1994
\TexasVIIIa; 541--550;
pi, hardy.ps :=
A multivariate form of Hardy's inequality and $L_p$-error bounds for multivariate Lagrange interpolation schemes
Shayne Waldron
August 1994
\SJMA; 28(1); 1997; 233--258;
pi, lift.ps :=
Integral error formul{\ae} for the scale of mean value interpolations which includes Kergin and Hakopian interpolation
Shayne Waldron
July 1994
\NM; 77(1); 1997; 105--122;
pi, hermite.ps :=
$L_p$-error bounds for Hermite interpolation and the associated Wirtinger inequalities
Shayne Waldron
May 1994
\CA; 13(4); 1997; 461--679;
pi, na, extremising.ps :=
Extremising the $L_p$-norm of a monic polynomial with roots in a given interval and Hermite interpolation
Shayne Waldron
May 1994
na, pi, polintelim.ps :=
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;
na, sphere.ps :=
Strictly positive definite functions on spheres
Amos Ron and Xingping Sun
February 1994
\MC; 65(216); 1996; 1513--1530;
fr, frame1.ps :=
Frames and stable bases for shift-invariant subspaces of $L_2(\Rd)$
Amos Ron and Zuowei Shen
February 1994
appeared in Canad. Math. J.
\CJM; 47(5); 1995; 1051--1094;
ao, pscattered.ps :=
$L^p$-approximation orders with scattered centres
Martin D. Buhmann and Amos Ron
January 1994
\ChamonixIIb; 93--112;
rb, sd, scattered.ps :=
Radial basis function approximation: from gridded centers to scattered centers
Nira Dyn and Amos Ron
November 1993
appeared in Proc. London Math. Soc. (1995)
\PLMS; 71(3); 1995; 76--108;
ao, si, approxloc.ps :=
Approximation orders of and approximation maps from local principal shift-invariant spaces
Amos Ron
May 1993
\JAT; 81(1); 1995; 38--65;
bs, na, boxeval.ps :=
On the evaluation of box splines,
Carl de Boor
March 1993
has appeared in Numer.Algorithms; 5; 1993; 5--23;
an alternative approach, particularly good for multiple directions, can be
found in Leif Kobbelt's paper
Stable evaluation of box splines;
\NA; 14(4); 1997; 377--382;
% available at
% http://www.mpi-sb.mpg.de/~kobbelt/papers/boxeval.ps.gz
% with the corresponding set of m-files at
% http://www.mpi-sb.mpg.de/~kobbelt/papers/boxeval.tgz
sr, ms, multpp.ps :=
Multivariate piecewise polynomials,
Carl de Boor
October 1992
has appeared in Acta Numerica; 2; 1993; 65--109;
wav2.ps :=
Multiresolution analysis by infinitely differentiable compactly supported functions
Nira Dyn, Amos Ron
September 1992
ACHA (1995)
rf, stablemask.ps :=
Characterizations of linear independence and stability of the shifts of a univariate refinable function in terms of its refinement mask
Amos Ron
September 1992
ao, sd, sct1.ps :=
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;
ao, aowoquasi.ps :=
Approximation order without quasi-interpolants
Carl de Boor
August 1992
has appeared in \TexasVII; 1--18;
di, ker.ps :=
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 Adv. Applied Math; 17; 1996; 209--250;
rb, ao, aoradial.ps :=
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;
ao, ms, aobivar.ps :=
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;
wv, wavelet.ps :=
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;
si, several.ps :=
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;
% minor correction in intro 01feb01
pi, na, polinterr.ps :=
On the error in multivariate polynomial interpolation
Carl de Boor
1991
has appeared in Applied Numerical Mathematics; 10; 1992; 297--305;
si, ao, l2shift.ps :=
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
ao, aoinfty.ps :=
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;
qi, ao, ms, quasiaprx.ps :=
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;
pi, leastsol.ps :=
The least solution for the polynomial interpolation problem;
Carl de Boor, Amos Ron
June 1990
has appeared in Math.Zeitschrift; 210; 1992; 347--378;
pi, na, compleast.html := http://www.ams.org/journals/mcom/1992-58-198/S0025-5718-1992-1122061-0/S0025-5718-1992-1122061-0.pdf
Computational aspects of polynomial interpolation in several variables
Carl de Boor, Amos Ron
March 1990
has appeared in Math.Comp.; 58; 1992; 705--727;
la, na, empty.ps :=
An empty exercise
Carl de Boor
March 1990
has appeared in
ACM SIGNUM Newsletter; 25(4); 1990; 2--6;
pi, sr, polintconte.ps :=
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;
sd, rb, djlr.ps :=
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.
ao, ms, qi, si, studia.ps :=
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.
la, modest.ps :=
An alternative approach to (the teaching of) rank and dimension
Carl de Boor
February 1990
has appeared in
\LAA; 146; 1991; 221--229;
ao, qi, quasi.ps :=
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;
al, ms, polideal.ps :=
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;
bs, boxtiling.ps :=
Carl de Boor, K. H"ollig
Box-spline tilings
May 1989
has appeared in \AMMo; 98; 1991; 793--802;
pi, bs, twopolspaces.ps :=
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)
al, bs, newideal.ps :=
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)
na,di, 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;
pi, multiint.ps :=
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)
pi, limorg.ps :=
The limit at the origin of a smooth function space;
Carl de Boor, Amos Ron
November 1988
has appeared in \TexasVI; 93--96;
su, cornercut.ps :=
Local corner cutting and the smoothness of the limiting curve;
Carl de Boor
November 1988
has appeared in \CAGD; 7; 1990; 389--397;
us, chebspline.ps :=
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;
si, csd1.ps :=
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.
ao, bs, pi, ebs4.ps :=
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
sr, ms, whatisspline.ps :=
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;
la, us, bsplloccond.ps :=
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).
us, bsplbasic.ps :=
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
ms, su, sr, birmingham.ps :=
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.
bs, us, BBform.ps :=
$B$--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.
si, polshift.ps :=
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)
ms, convcardseries.h := http://www.ams.org/journals/proc/1986-098-03/S0002-9939-1986-0857940-1/S0002-9939-1986-0857940-1.pdf
Convergence of cardinal series;
Carl de Boor, Klaus H\"ollig, Sherman Riemenschneider
August 1985
has appeared: \PAMS; 98(3); 1986; 457--460;
us, notaknot.ps :=
Convergence of cubic spline interpolation with the not-a-knot condition
Carl de Boor
1985
MRC TSR 2876, October 1985
ao, partitions_of_unity.html := http://www.ams.org/journals/proc/1985-093-04/S0002-9939-1985-0776207-2/S0002-9939-1985-0776207-2.pdf
Partitions of unity and approximation
Carl de Boor and Ronald DeVore
May 1984
has appeared in \PAMS; 93(4); 1985; 705--709;
us, tpproof.html := http://www.ams.org/journals/mcom/1985-45-172/S0025-5718-1985-0804938-2/S0025-5718-1985-0804938-2.pdf
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;
ms, convbivcard.pdf :=
Convergence of bivariate cardinal interpolation;
C. de Boor, K. H\"ollig, S. Riemenschneider
1984
has appeared in \CA; 1; 1985; 183--193;
ao, contrapp.ps :=
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
ms, bs, si, 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;
ao, c1counter.html := http://www.jstor.org/view/00029939/di970906/97p1141m/0?config=jstor&frame=noframe
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;
ao, ms, approxorder.html := http://www.math.tamu.edu/~rdevore/publications/40.pdf
Approximation order from smooth bivariate splines
C. de Boor, R. DeVore, K. H\"ollig
1982
has appeared in TexasIV; 353--357;
ao, ms, sr, lancaster_lectures.pdf :=
Topics in multivariate approximation theory
C. de Boor
May 1982
TSR #2379, Mathematics Research Center, University of Wisconsin-Madison
ao, ms, qi, boxsplinestart.html := http://www.ams.org/journals/tran/1983-276-02/S0002-9947-1983-0688977-5/S0002-9947-1983-0688977-5.pdf
Approximation by smooth multivariate splines
Carl de Boor and Ron DeVore
December 1981
has appeared in \TAMS; 276(2); 1983; 775--788;
la, infsignreg.html := http://www.ams.org/journals/tran/1982-274-01/S0002-9947-1982-0670918-7/S0002-9947-1982-0670918-7.pdf
Inverses of infinite sign regular matrices
C. de Boor, S. Friedland, and A. Pinkus
November 1980
has appeared: \TAMS; 274(1); 1982; 59--68;
ms, multirecur.html := http://www.ams.org/journals/proc/1982-085-03/S0002-9939-1982-0656111-8/S0002-9939-1982-0656111-8.pdf
Recurrence relations for multivariate B-splines
Carl de Boor and Klaus H\"ollig
May 1981
has appeared: \PAMS; 85(3); 1982; 397--400;
la, inversebiinfband.html := http://www.ams.org/journals/tran/1982-274-01/S0002-9947-1982-0670917-5/S0002-9947-1982-0670917-5.pdf
The inverse of a totally positive bi-infinite band matrix
C. de Boor
November 1980
has appeared: \TAMS; 274(1); 1982; 45--58;
na, us, superconvergence.html := http://www.ams.org/journals/mcom/1981-36-153/S0025-5718-1981-0595039-6/S0025-5718-1981-0595039-6.pdf
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;
us, maxnormbound.ps :=
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;
na, us, colloceignumer.html := http://www.ams.org/journals/mcom/1981-36-153/S0025-5718-1981-0595038-4/S0025-5718-1981-0595038-4.pdf
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;
na, us, colloceigprinc.html := http://www.ams.org/journals/mcom/1980-35-151/S0025-5718-1980-0572849-1/S0025-5718-1980-0572849-1.pdf
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;
ao, nwidth.html := http://www.ams.org/journals/proc/1980-080-04/S0002-9939-1980-0587931-4/S0002-9939-1980-0587931-4.pdf
C. de Boor, R. DeVore, K. H\"ollig
Mixed norm $n$-widths
March 1979
has appeared in \PAMS; 80(4); 1980; 577--583;
ms, 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;
us, agee.ps :=
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;
la, 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;
na, la, countcomp.html := http://www.ams.org/journals/mcom/1977-31-140/S0025-5718-1977-0501939-4/S0025-5718-1977-0501939-4.pdf
Comments on the comparison of global methods for linear two-point boundary
value problems;
Carl de Boor and Blair Swartz
summer 1977
has appeared in \MC; 31(140); 1977; 916--921;
sr, us, survey76.ps :=
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
us, oddbiinf.ps :=
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;
us, l2inlinfconj.html := http://http://www.ams.org/journals/mcom/1976-30-136/S0025-5718-1976-0425432-1/S0025-5718-1976-0425432-1.pdf
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
us, 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;
us, loclinfl.ps :=
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;
us, budanfourier.ps :=
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
us, smallderiv.ps :=
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;
us, howsmall.ps :=
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
us, cubicnullspline.pdf :=
On cubic spline functions that vanish at all knots;
Carl de Boor
1973
\AiM, 20(1), 1976, 1--17;
us, perfect_spline.html := http://www.ams.org/journals/bull/1974-80-04/S0002-9904-1974-13572-X/S0002-9904-1974-13572-X.pdf
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
us, tp.pdf :=
Total positivity of the spline collocation matrix;
Carl de Boor;
1974
\JMM, 25(6), 1976, 724--727;
us, splbound.ps :=
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
qi, us, quasiint.ps :=
The quasi-interpolant as a tool in elementary polynomial spline theory;
Carl de Boor
1973
has appeared in \TexasI; 269--276;
us, ao, na, goodappr.ps :=
Good approximation by splines with variable knots;
Carl de Boor
1973
has appeared in \EdmontonI; 57--72;
us, nonnegcoefs.html := http://www.ams.org/journals/mcom/1974-28-126/S0025-5718-1974-0378357-2/S0025-5718-1974-0378357-2.pdf
Carl de Boor and James W. Daniel
Splines with nonnegative $B$-spline coefficients
april 1973
has appeared: \MC; 28(126); 1974; 565--568;
us, na, 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.
us, bsplcalc.pdf :=
On calculating with $B$-splines;
Carl de Boor
september 1970
\JAT; 6; 1972; 50--62;
ao, us, gamma.ps :=
On the approximation by $\gamma$-polynomials;
Carl de Boor
1969
has appeared in \MadisonII; 157--183;
qi, ao, us, unifappr.ps :=
On uniform approximation by splines
Carl de Boor
1967
has appeared as \JAT; 1; 1968; 219--235;
4oct08 various misprints have been corrected
us, na, tr20.ps :=
Least Squares Cubic Spline Approximation I -- Fixed Knots
Carl de Boor, John R. Rice
CSD TR 20 April 1968
us, na, tr21.ps :=
Least Squares Cubic Spline Approximation II -- Variable Knots
Carl de Boor, John R. Rice
CSD TR 21 April 1968
% error in NUBAS corrected 3oct01
us, ao, spaprmom.pdf :=
On local spline approximation by moments;
Carl de Boor
Sep 1966
has appeared in
\JMM; 17; 1968; 729--735;
us, deboorphd.ps :=
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
us, lynch.ps :=
On splines and their minimum properties;
Carl de Boor and Robert E. Lynch
1965
has appeared in
\JMM; 15; 1966; 953--969;
us, 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
us, birkhoff_error.pdf :=
Error bounds for spline interpolation;
Garrett Birkhoff & Carl de Boor;
1964
\JMM, 13(5), 1964, 827--835;
sr, us, ms, 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;
us, ao, baoddspline.pdf :=
Best approximation properties of spline functions of odd degree;
Carl de Boor;
1963
\JMM, 12(5), 1963, 747--750;
ms, na, 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;
TeX, viva_vi.ps :=
Viva vi!, (a brief introduction to vi)
Carl de Boor
1987
version: 03aug03
TeX, intro.ps :=
TeXnicalities (an informal introduction to TeX use) (the odd pages)
Carl de Boor
1987
version: 06feb99
TeX, ttintro.ps :=
TeXnicalities (an informal introduction to TeX use) (the even pages)
Carl de Boor
1987
version: 06feb99
TeX, 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
TeX, verbatim.tex :=
A file of plain TeX macros useful for handling the typesetting of programs and program-related material in plain TeX.
Carl de Boor
1991
version: 25feb98
TeX, index.tex :=
A file of plain TeX macros useful for generating (the draft of) an index.
Carl de Boor
1993
version: 27jun98
TeX, journal.tex :=
TeX macros of use with the spline bibliography.
Carl de Boor
1990
version: 05jun04
TeX, proceed.tex :=
TeX macros of use with the spline bibliography.
Carl de Boor
1990
version: 02may04
TeX, refmac.tex :=
TeX macros of use with the spline bibliography.
Carl de Boor
1990
version: 27may04
TeX, message.mm :=
a self-unwrapping wrapper containing files for simplifying the safe mailing of files via email.
Carl de Boor
1989
version: mar 96
us, isobib.ps :=
List of publications of I. J. Schoenberg
(Carl de Boor)
1987
updated 10mar09