IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII AAA_readme IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII ------------------------------------------------------------------------------- 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_III.pdf := Elastic Splines III: Existence of stable nonlinear splines; Albert Borb\'ely & Michael J. Johnson december 2018; us, ns, Elastic_Splines_II_final.pdf := Elastic Splines II: Unicity of optimal s-curves and curvature continuity; Albert Borb\'ely & Michael J. Johnson august 2017 al, bs, di, ms, idl16.pdf := Complete graphs: the space of simplicial cones, and their path tree representation; Amos Ron & Shengnan (Sarah) Wang august 2017 al, bs, di, ms, idl13.pdf := Bivariate truncated powers: complete intersection decompositions and the spline representation; Amos Ron & Shengnan (Sarah) Wang june 2017 al, bs, di, ms, idl12.pdf := Truncated power splines: acyclic resolutions of cone polynomials; Amos Ron & Shengnan (Sarah) Wang june 2017 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, sr, re_quak.pdf := A comment on Ewald Quak's "About B-splines"; Carl de Boor october 2016 \JNAAT;45(1); 2016; 84--86; 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, deboor2.pdf := 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; us, ns, Golomb_1978_remastered.pdf := Stability of interpolating elastica; Michael Golomb may 1978 has appeared as: MRC TSR #1852; 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