Approximation Theory XV: San Antonio 2016 PDF
Preview Approximation Theory XV: San Antonio 2016
Springer Proceedings in Mathematics & Statistics Gregory E. Fasshauer Larry L. Schumaker E ditors Approximation Theory XV: San Antonio 2016 Springer Proceedings in Mathematics & Statistics Volume 201 Springer Proceedings in Mathematics & Statistics This book series features volumes composed of selected contributions from workshops and conferences in all areas of current research in mathematics and statistics, including operation research and optimization. In addition to an overall evaluation of the interest, 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 mathematical and statistical research today. More information about this series at http://www.springer.com/series/10533 Gregory E. Fasshauer Larry L. Schumaker (cid:129) Editors Approximation Theory XV: San Antonio 2016 123 Editors Gregory E. Fasshauer Larry L.Schumaker Department ofApplied Mathematics and Department ofMathematics Statistics Vanderbilt University ColoradoSchool ofMines Nashville, TN Golden,CO USA USA ISSN 2194-1009 ISSN 2194-1017 (electronic) SpringerProceedings in Mathematics& Statistics ISBN978-3-319-59911-3 ISBN978-3-319-59912-0 (eBook) DOI 10.1007/978-3-319-59912-0 LibraryofCongressControlNumber:2017943223 MathematicsSubjectClassification(2010): 41-XX,42-XX,65-XX,42C05,65D07,94A12 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland Preface These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation TheoryheldatvariouslocationsintheUSAandwasattendedby146participants. 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, 2013). We are particularly indebted to our plenary speakers: Josef Dick (Univ. New South Wales), Simon Foucart (Texas A&M), Elisabeth Larsson (Uppsala Univ.), Doron Lubinsky (Georgia Tech), Carla Manni (Univ. Rome—Tor Vergata), Mike Neamtu (Vanderbilt Univ.), and Ulrich Reif (Tech. Univ. Darmstadt). The eighth Vasil A. Popov Prize in Approximation Theory was awarded to Jean-Marie Mirebeau (CNRS, Université Paris-Sud), who also presented a plenary lecture. Thanks are also due to the presenters of contributed papers, as well as everyone who attended for making the conference a success. We are especially grateful to the National Science Foundation for financial support,andalsototheDepartmentofMathematicsatVanderbiltUniversityforits logistical support. Wewouldalsoliketoexpressoursinceregratitudetothereviewerswhohelped select articles for inclusion in this proceedings volume, and also for their sugges- tions to the authors for improving their papers. Golden, CO, USA Gregory E. Fasshauer Nashville, TN, USA Larry L. Schumaker v Contents Linear Barycentric Rational Interpolation with Guaranteed Degree of Exactness .... .... ..... .... .... .... .... .... ..... .... 1 Jean-Paul Berrut Approximation by C1 Splines on Piecewise Conic Domains.. ..... .... 21 Oleg Davydov and Wee Ping Yeo A Rescaled Method for RBF Approximation . .... .... .... ..... .... 39 Stefano De Marchi, Andrea Idda and Gabriele Santin Flavors of Compressive Sensing.... .... .... .... .... .... ..... .... 61 Simon Foucart Computing with Functions on Domains with Arbitrary Shapes ... .... 105 Daan Huybrechs and Roel Matthysen A Polygonal Spline Method for General Second-Order Elliptic Equations and Its Applications .... .... .... .... .... .... ..... .... 119 Ming-Jun Lai and James Lanterman An Adaptive Triangulation Method for Bivariate Spline Solutions of PDEs .. .... .... .... .... ..... .... .... .... .... .... ..... .... 155 Ming-Jun Lai and Clayton Mersmann Refinable Functions with PV Dilations .. .... .... .... .... ..... .... 177 Wayne Lawton Polyhyperbolic Cardinal Splines ... .... .... .... .... .... ..... .... 189 Jeff Ledford Adaptive Computation with Splines on Triangulations with Hanging Vertices .. .... ..... .... .... .... .... .... ..... .... 197 Shiying Li and Larry L. Schumaker vii viii Contents Scaling Limits of Polynomials and Entire Functions of Exponential Type .... .... ..... .... .... .... .... .... ..... .... 219 D.S. Lubinsky Generalized B-Splines in Isogeometric Analysis ... .... .... ..... .... 239 Carla Manni, Fabio Roman and Hendrik Speleers On Polynomials with Vanishing Hessians and Some Density Problems .. .... .... ..... .... .... .... .... .... ..... .... 269 Tom McKinley and Boris Shekhtman Batched Stochastic Gradient Descent with Weighted Sampling.... .... 279 Deanna Needell and Rachel Ward A Fractional Spline Collocation Method for the Fractional-order Logistic Equation .. .... .... ..... .... .... .... .... .... ..... .... 307 Francesca Pitolli and Laura Pezza The Complete Length Twelve Parametrized Wavelets.. .... ..... .... 319 David W. Roach Potential Theoretic Approach to Design of Accurate Numerical Integration Formulas in Weighted Hardy Spaces.. .... .... ..... .... 335 Ken’ichiro Tanaka, Tomoaki Okayama and Masaaki Sugihara A Class of Intrinsic Trigonometric Mode Polynomials.. .... ..... .... 361 Vesselin Vatchev Kernel-Based Approximation Methods for Partial Differential Equations: Deterministic or Stochastic Problems?. .... .... ..... .... 375 Qi Ye Contributors Jean-Paul Berrut Department of Mathematics, University of Fribourg, Fribourg, Switzerland Oleg Davydov Department of Mathematics, University of Giessen, Giessen, Germany Stefano De Marchi DepartmentofMathematics“TullioLevi-Civita”,University of Padova, Padova, Italy Simon Foucart Department of Mathematics, Texas A&M University, College Station, TX, USA Daan Huybrechs KU Leuven, Leuven, Belgium Andrea Idda Banco Popolare, Verona, Italy Ming-Jun Lai Department of Mathematics, University of Georgia, Athens, GA, USA James Lanterman Department of Mathematics, University of Georgia, Athens, GA, USA Wayne Lawton School of Mathematics & Statistics, University of Western Australia, Perth, Australia Jeff Ledford Virginia Commonwealth University, Richmond, VA, USA Shiying Li Department of Mathematics, Vanderbilt University, Nashville, TN, USA D.S. Lubinsky School of Mathematics, Georgia Institute of Technology, Atlanta, GA, USA Carla Manni Department of Mathematics, University of Rome “Tor Vergata”, Rome, Italy Roel Matthysen KU Leuven, Leuven, Belgium ix x Contributors Tom McKinley University of South Florida, Tampa, FL, USA Clayton Mersmann Department of Mathematics, University of Georgia, Athens, GA, USA Deanna Needell Claremont McKenna College, Claremont, CA, USA Tomoaki Okayama Department of Systems Engineering, Graduate School of InformationSciences,HiroshimaCityUniversity,Asaminami-ku,Hiroshima,Japan LauraPezza DipartimentoSBAI,UniversitàdiRoma“LaSapienza”,Roma,Italy Francesca Pitolli Dipartimento SBAI, Università diRoma “La Sapienza”, Roma, Italy David W. Roach Murray State University, Murray, KY, USA Fabio Roman Department of Mathematics, University of Turin, Turin, Italy Gabriele Santin IANS University of Stuttgart, Stuttgart, Germany Larry L. Schumaker Department of Mathematics, Vanderbilt University, Nashville, TN, USA Boris Shekhtman University of South Florida, Tampa, FL, USA Hendrik Speleers Department of Mathematics, University of Rome “Tor Vergata”, Rome, Italy Masaaki Sugihara Department of Physics and Mathematics, College of Science and Engineering, Aoyama Gakuin University, Chuo-ku, Sagamihara-shi, Kanagawa, Japan Ken’ichiroTanaka DepartmentofMathematicalInformatics,GraduateSchoolof Information Science and Technology, The University of Tokyo, Bunkyo-ku, Tokyo, Japan VesselinVatchev SchoolofMathematicalandStatisticalSciences,TheUniversity of Texas Rio Grande Valley, Brownsville, TX, USA Rachel Ward University of Texas, Austin, TX, USA Qi Ye School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong, China WeePingYeo FacultyofScience,UniversitiBruneiDarussalam,Gadong,Brunei Darussalam
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