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Birkhäuser

Numerical Methods in Approximation Theory, Vol. 9

  • Book
  • © 1992

Overview

Editors:
  1. Dietrich Braess

    1. Fakultät und Institut für Mathematik, Ruhr-Universität Bochum, Bochum 1, Germany

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    You can also search for this editor in PubMed   Google Scholar

  2. Larry L. Schumaker

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

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: International Series of Numerical Mathematics (ISNM, volume 105)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Blending Approximations with Sine Functions

    • G. Baszenski, F.-J. Delvos, S. Jester
    Pages 1-19

  3. Quasi-interpolation in the Absence of Polynomial Reproduction

    • R. K. Beatson, W. A. Light
    Pages 21-39

  4. Estimating the Condition Number for Multivariate Interpolation Problems

    • P. Binev, K. Jetter
    Pages 41-52

  5. Wavelets on a Bounded Interval

    • Charles K. Chui, Ewald Quak
    Pages 53-75

  6. Quasi-Kernel Polynomials and Convergence Results for Quasi-Minimal Residual Iterations

    • Roland W. Freund
    Pages 77-95

  7. Rate of Approximation of Weighted Derivatives by Linear Combinations of SMD Operators

    • Margareta Heilmann
    Pages 97-115

  8. Approximation by Multivariate Splines: an Application of Boolean Methods

    • Rong-Qing Jia
    Pages 117-134

  9. Lm,ℓ,s-splines in ℝd

    • A. Le Méhauté, A. Bouhamidi
    Pages 135-154

  10. Constructive Multivariate Approximation with Sigmoidal Functions and Applications to Neural Networks

    • Burkhard Lenze
    Pages 155-175

  11. Spline-Wavelets of Minimal Support

    • T. Lyche, K. Mørken
    Pages 177-194

  12. Necessary Conditions for Local Best Chebyshev Approximations by Splines with Free Knots

    • Bernd Mulansky
    Pages 195-206

  13. C1 Interpolation on Higher-Dimensional Analogues of the 4-Direction Mesh

    • Andy Neff, Jörg Peters
    Pages 207-220

  14. Tabulation of Thin Plate Splines on a Very Fine Two-Dimensional Grid

    • M. J. D. Powell
    Pages 221-244

  15. The L2-Approximation Orders of Principal Shift-Invariant Spaces Generated by a Radial Basis Function

    • Amos Ron
    Pages 245-268

  16. A Multi-Parameter Method for Nonlinear Least-Squares Approximation

    • R. Schaback
    Pages 269-283

  17. Analog VLSI Networks

    • Walter Schempp
    Pages 285-300

  18. Converse Theorems for Approximation on Discrete Sets II

    • G. Schmeisser
    Pages 301-316

  19. A Dual Method for Smoothing Histograms Using Nonnegative C1-Splines

    • Jochen W. Schmidt
    Pages 317-329

  20. Segment Approximation Using Linear Functionals

    • Manfred Sommer
    Pages 331-346
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Keywords

About this book

This book is the official proceedings of a conference on Numerical Methods in Approximation Theory which was held at the Mathematisches Forschungs­ institut in Oberwolfach during the week of November 24~30, 1991. It contains refereed and edited papers by 20 of the 49 participants. The book is dedicated to the memory of Prof. Lothar Collatz who main­ tained a long and active interest in numerical approximation. It is the ninth in a series of volumes published by Birkhiiuser resulting from conferences on the subject held at Oberwolfach, and co-organized by Prof. Collatz. We now briefly describe the contents of the book. The paper of BASZEN­ SKI, DELVOS and JESTER deals with blending using sine double series expan­ sions of functions defined on the unit square. In addition to giving explicit error estimates for partial sums and for interpolating sine polynomials, they also show that Boolean sums yield almost the same asymptotic error estimates as the conventional tensor-product approach, but with a reduced number of terms. The paper of BEATSON and LIGHT discusses approximation by quasi­ interpolants which are sums of scaled translates of a one-parameter family of functions. They do not require reproduction of low degree polynomials, but nevertheless are able to give error bounds and analyze quasi-interpolation based on Gaussians and exponentials. BINEV and JETTER deal with multivariate interpolation using shifts of a single basis function. They treat both gridded data and scattered data. As examples, they consider box splines and certain radial basis functions.

Editors and Affiliations

  • Fakultät und Institut für Mathematik, Ruhr-Universität Bochum, Bochum 1, Germany

    Dietrich Braess

  • Dept. of Mathematics, Vanderbilt University, Nashville, USA

    Larry L. Schumaker

Bibliographic Information

  • Book Title: Numerical Methods in Approximation Theory, Vol. 9

  • Editors: Dietrich Braess, Larry L. Schumaker

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-8619-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1992

  • Hardcover ISBN: 978-3-7643-2746-0Published: 01 August 1992

  • Softcover ISBN: 978-3-0348-9702-0Published: 30 October 2012

  • eBook ISBN: 978-3-0348-8619-2Published: 11 March 2013

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: XIV, 359

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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