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Approximation Theory XVI

Nashville, TN, USA, May 19-22, 2019

  • Conference proceedings
  • © 2021

Overview

Editors:
  1. Gregory E. Fasshauer

    1. Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, USA

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  2. Marian Neamtu

    1. Department of Mathematics, Vanderbilt University, Nashville, USA

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    You can also search for this editor in PubMed   Google Scholar

  3. Larry L. Schumaker

    1. Department of Mathematics, Vanderbilt University, Nashville, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Includes survey articles on nonstationary subdivision and Prony’s method
  • Includes 11 research papers on approximation theory
  • Covers both theory and applications of approximation theory

Part of the book series: Springer Proceedings in Mathematics & Statistics (PROMS, volume 336)

Included in the following conference series:

Conference proceedings info: AT 2019.

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Table of contents (13 papers)

  1. Front Matter

    Pages i-viii
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  2. Time-Variant System Approximation via Later-Time Samples

    • Roza Aceska, Yeon Hyang Kim
    Pages 1-9

  3. C1-Quartic Butterfly-Spline Interpolation on Type-1 Triangulations

    • Domingo Barrera, Costanza Conti, Catterina Dagnino, María José Ibáñez, Sara Remogna
    Pages 11-26

  4. Approximation with Conditionally Positive Definite Kernels on Deficient Sets

    • Oleg Davydov
    Pages 27-38

  5. Non-stationary Subdivision Schemes: State of the Art and Perspectives

    • Costanza Conti, Nira Dyn
    Pages 39-71

  6. Cubature Rules Based on Bivariate Spline Quasi-Interpolation for Weakly Singular Integrals

    • Antonella Falini, Tadej Kanduč, Maria Lucia Sampoli, Alessandra Sestini
    Pages 73-86

  7. On DC Based Methods for Phase Retrieval

    • Meng Huang, Ming-Jun Lai, Abraham Varghese, Zhiqiang Xu
    Pages 87-121

  8. Modifications of Prony’s Method for the Recovery and Sparse Approximation with Generalized Exponential Sums

    • Ingeborg Keller, Gerlind Plonka
    Pages 123-152

  9. On Eigenvalue Distribution of Varying Hankel and Toeplitz Matrices with Entries of Power Growth or Decay

    • Gidon Kowalsky, Doron S. Lubinsky
    Pages 153-170

  10. On the Gradient Conjecture for Quadratic Polynomials

    • Tom McKinley, Boris Shekhtman
    Pages 171-179

  11. Balian-Low Theorems in Several Variables

    • Michael Northington V, Josiah Park
    Pages 181-206

  12. Quasi-Interpolant Operators and the Solution of Fractional Differential Problems

    • Enza Pellegrino, Laura Pezza, Francesca Pitolli
    Pages 207-218

  13. Stochastic Collocation with Hierarchical Extended B-Splines on Sparse Grids

    • Michael F. Rehme, Dirk Pflüger
    Pages 219-236

  14. Trivariate Interpolated Galerkin Finite Elements for the Poisson Equation

    • Tatyana Sorokina, Shangyou Zhang
    Pages 237-249

  15. Back Matter

    Pages 251-253
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  1. Approximation Theory XVI

Keywords

About this book

These proceedings are based on the international conference Approximation Theory XVI held on May 19–22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States.  Over 130 mathematicians from 20 countries attended.  The book contains two longer survey papers on nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. The book should be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.

Editors and Affiliations

  • Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, USA

    Gregory E. Fasshauer

  • Department of Mathematics, Vanderbilt University, Nashville, USA

    Marian Neamtu, Larry L. Schumaker

About the editors

Gregory E. Fasshauer is Professor and Head of the Applied Mathematics and Statistics Department at the Colorado School of Mines. He is the author of two books on kernel-based approximation methods, and co-editor of three proceedings volumes. His research is concerned with the theory and applications of kernel-based approximation methods in approximation theory, numerical analysis, data fitting and machine learning.

Marian Neamtu is Professor and Chair of the Department of Mathematics at Vanderbilt University. His current research interests are in approximation theory, splines, geometric design, and numerical analysis.

Larry L. Schumaker is Stevenson Professor of Mathematics at Vanderbilt University.  He is a fellow of the AMS, a SIAM fellow, and a member of the Norwegian Academy of Sciences.  He is the author of three books on splines, and is a co-editor of over 40 proceedings volumes.  He continues to do research on splines and their applications.

Bibliographic Information

  • Book Title: Approximation Theory XVI

  • Book Subtitle: Nashville, TN, USA, May 19-22, 2019

  • Editors: Gregory E. Fasshauer, Marian Neamtu, Larry L. Schumaker

  • Series Title: Springer Proceedings in Mathematics & Statistics

  • DOI: https://doi.org/10.1007/978-3-030-57464-2

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-57463-5Published: 05 January 2021

  • Softcover ISBN: 978-3-030-57466-6Published: 06 January 2022

  • eBook ISBN: 978-3-030-57464-2Published: 04 January 2021

  • Series ISSN: 2194-1009

  • Series E-ISSN: 2194-1017

  • Edition Number: 1

  • Number of Pages: VIII, 253

  • Number of Illustrations: 5 b/w illustrations, 36 illustrations in colour

  • Topics: Approximations and Expansions

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