Approximation Theory XIV: San Antonio 2013 PDF
Preview Approximation Theory XIV: San Antonio 2013
Springer Proceedings in Mathematics & Statistics Gregory E. Fasshauer Larry L. Schumaker E ditors Approximation Theory XIV: San Antonio 2013 Springer Proceedings in Mathematics & Statistics Volume 83 For furthervolumes: http://www.springer.com/series/10533 Springer Proceedings in Mathematics & Statistics Thisbookseriesfeaturesvolumescomposedofselectcontributionsfromworkshops and conferences in all areas of current research in mathematics and statistics, includingORandoptimization.Inadditiontoanoverallevaluationoftheinterest, scientific quality, and timeliness of each proposal at the hands of the publisher, individual contributions are all refereed to the high quality standards of leading journals in the field. Thus, this series provides the research community with well-edited, authoritative reports on developments in the most exciting areas of mathematicalandstatisticalresearchtoday. Gregory E. Fasshauer Larry L. Schumaker • Editors Approximation Theory XIV: San Antonio 2013 123 Editors Gregory E.Fasshauer LarryL. Schumaker Department of AppliedMathematics Department of Mathematics IllinoisInstitute ofTechnology VanderbiltUniversity Chicago, IL Nashville, TN USA USA ISSN 2194-1009 ISSN 2194-1017 (electronic) ISBN 978-3-319-06403-1 ISBN 978-3-319-06404-8 (eBook) DOI 10.1007/978-3-319-06404-8 Springer ChamHeidelberg New YorkDordrecht London MathematicsSubjectClassification(2010):65D07,65T60,47B06,32E30,41Axx (cid:2)SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe work. Duplication of this publication or parts thereof is permitted only under the provisions of theCopyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the CopyrightClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Preface These proceedings are based on papers presented at the international conference Approximation Theory XIV, which was held April 7–10, 2013 in San Antonio, Texas.TheconferencewasthefourteenthinaseriesofmeetingsinApproximation Theory held at various locations in the United States, and was attended by 133 participants. Previous conferences in the series were held in Austin, Texas (1973, 1976, 1980, 1992), College Station, Texas (1983, 1986, 1989, 1995), Nashville, Tennessee (1998), St. Louis, Missouri (2001), Gatlinburg, Tennessee (2004), and San Antonio, Texas (2007, 2010). We are particularly indebted to our plenary speakers: Peter Binev (South Carolina),AnnalisaBuffa(Pavia),MichaelFloater(Oslo),KaiHormann(Lugano), Gitta Kutyniok (Berlin), Grady Wright (Boise), and Yuan Xu (Oregon) for their very fine expository talks outlining new research areas. The seventh Vasil A. Popov Prize in Approximation Theory was awarded to Andriy Bondarenko (Kiev),whoalsopresentedaplenarylecture.Thanksarealsoduetothepresenters ofcontributedpapers,aswellaseveryonewhoattendedformakingtheconference a success. We are especially grateful to the National Science Foundation for financial support, and also to the Department of Mathematics at Vanderbilt University for its logistical support. Wewouldalsoliketoexpressoursinceregratitudetothereviewerswhohelped select articles for inclusion in this proceedings volume, and also for their sug- gestions to the authors for improving their papers. Gregory E. Fasshauer Larry L. Schumaker v Contents Isogeometric Method for the Elliptic Monge-Ampère Equation. . . . . . 1 Gerard Awanou Dual Compatible Splines on Nontensor Product Meshes. . . . . . . . . . . 15 L. Beirão da Veiga, A. Buffa, G. Sangalli and R. Vázquez Multivariate Anisotropic Interpolation on the Torus. . . . . . . . . . . . . . 27 Ronny Bergmann and Jürgen Prestin A Generalized Class of Hard Thresholding Algorithms for Sparse Signal Recovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Jean-Luc Bouchot On a New Proximity Condition for Manifold-Valued Subdivision Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Tom Duchamp, Gang Xie and Thomas Yu Wachspress and Mean Value Coordinates . . . . . . . . . . . . . . . . . . . . . 81 Michael S. Floater Hermite and Bernstein Style Basis Functions for Cubic Serendipity Spaces on Squares and Cubes . . . . . . . . . . . . . . . . . . . . . 103 Andrew Gillette Suitability of Parametric Shepard Interpolation for Nonrigid Image Registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 A. Ardeshir Goshtasby Parabolic Molecules: Curvelets, Shearlets, and Beyond. . . . . . . . . . . . 141 Philipp Grohs, Sandra Keiper, Gitta Kutyniok and Martin Schäfer vii viii Contents Microlocal Analysis of Singularities from Directional Multiscale Representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 Kanghui Guo, Robert Houska and Demetrio Labate Barycentric Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Kai Hormann Numerical Determination of Extremal Points and Asymptotic Order of Discrete Minimal Riesz Energy for Regular Compact Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Manuel Jaraczewski, Marco Rozgi(cid:2)c and Marcus Stiemer Eigenvalue Sequences of Positive Integral Operators and Moduli of Smoothness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 T. Jordão, V. A. Menegatto and Xingping Sun Reconstructing Multivariate Trigonometric Polynomials from Samples Along Rank-1 Lattices. . . . . . . . . . . . . . . . . . . . . . . . . 255 Lutz Kämmerer On Nondegenerate Rational Approximation. . . . . . . . . . . . . . . . . . . . 273 L. Franklin Kemp Multivariate C1-Continuous Splines on the Alfeld Split of a Simplex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Alexei Kolesnikov and Tatyana Sorokina On Convergence of Singular Integral Operators with Radial Kernels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Sevilay Kırcı Serenbay, Özge Dalmanog˘lu and Ertan I_bikli Lower Bound on the Dimension of Trivariate Splines on Cells . . . . . . 309 Jianyun Jimmy Shan One Characterization of Lagrange Projectors. . . . . . . . . . . . . . . . . . . 335 Boris Shekhtman Minimal Versus Orthogonal Projections onto Hyperplanes in ‘n and ‘n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343 1 ‘ Boris Shekhtman and Lesław Skrzypek On Hermite Interpolation by Splines with Continuous Third Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 Vesselin Vatchev Contents ix Best Polynomial Approximation on the Unit Sphere and the Unit Ball. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 Yuan Xu Support Vector Machines in Reproducing Kernel Hilbert Spaces Versus Banach Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 Qi Ye Contributors Gerard Awanou Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Chicago, IL, USA Ronny Bergmann Department of Mathematics, University Kaiserslautern, Kaiserslautern, Germany Jean-LucBouchot DepartmentofMathematics,DrexelUniversity,Philadelphia, PA, USA A. Buffa Istituto di Matematica Applicata e Tecnologie Informatiche ‘E. Magenes’ del CNR, Pavia, Italy L. Beirão da Veiga Dipartimento di Matematica, Università di Milano, Milano, Italy ÖzgeDalmanog˘lu FacultyofEducation,DepartmentofMathematicsEducation, Ba(cid:2)skent University, Ankara, Turkey Tom Duchamp Department of Mathematics, University of Washington, Seattle, WA, USA Michael S. Floater Department of Mathematics, University of Oslo, Oslo, Norway Andrew Gillette Department of Mathematics, University of Arizona, Tucson, AZ, USA A. Ardeshir Goshtasby Department of Computer Science and Engineering, Wright State University, Dayton, OH, USA Philipp Grohs Seminar for Applied Mathematics, ETH Zürich, Zürich, Switzerland Kanghui Guo Missouri State University, Springfield, MO, USA KaiHormann FacultyofInformatics,UniversitàdellaSvizzeraitaliana,Lugano, Switzerland Robert Houska Department of Mathematics, University of Houston, Houston, TX, USA xi
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