Approximation Theory XV: San Antonio 2016

401 Pages·2017·10.83 MB·English

by  Gregory E. Fasshauer

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
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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
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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