Quantitative Approximation

Quantitative Approximation

Proceedings of a Symposium on Quantitative Approximation Held in Bonn, West Germany, August 20-24, 1979

1st Edition - January 28, 1980

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  • Editors: Ronald A. Devore, Karl Scherer
  • eBook ISBN: 9781483265124

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Quantitative Approximation provides information pertinent to nonlinear approximation, including rational approximation and optimal knot spline approximation. This book discusses spline approximation with the most emphasis on multivariate and knot independent questions. Organized into 26 chapters, this book begins with an overview of the inequality for the sharp function in terms of the maximal rearrangement. This text then examines the best co-approximation in a Hilbert space wherein the existence ad uniqueness sets are the closed flats. Other chapters consider the inverse of the coefficient matrix for the system satisfied by the B-spline coefficients of the cubic spline interpolant at knots. This book discusses as well the relationship between the structural properties of a function and its degree of approximation by rational functions. The final chapter deals with the problem of existence of continuous selections for metric projections and provides a solution for this problem. This book is a valuable resource for mathematicians.

Table of Contents

  • Contributors


    On an Inequality for the Sharp Function

    On the Best Co-Approximation in a Hilbert Space

    What Is the Main Diagonal of a Biinfinite Band Matrix?

    Rational Approximation and Exotic Lipschitz Spaces

    Some Mathematical Properties of Empirical Gibbs Functions

    Multivariate Interpolation and the Radon Transform, Part II: Some Further Examples

    Lacunary Trigonometric Interpolation on Equidistant Nodes

    Monotone Approximation by Spline Functions

    Approximation by Smooth Multivariate Splines on Nonuniform Grids

    Approximation by Small Rank Tensor Products of Splines

    Variable Knot, Variable Degree Spline Approximation to xβ

    On Sharp Necessary Conditions for Radial Fourier Multipliers

    Approximating Bivariate Functions and Matrices by Nomographic Functions

    L∞-Bounds of L2-Projections on Splines

    Diameters of Classes of Smooth Functions

    On Estimates of Diameters

    Bounds for the Error in Trigonometric Hermite Interpolation

    Birkhoff Interpolation: Some Applications of Coalescence

    n-Widths of Octahedra

    The Approximation of Multiple Integrals by Using Interpolatory Cubature Formulae

    Interpolatory Cubature Formulae and Real Ideals

    Strong Uniqueness of Best Approximations and Weak Chebyshev Systems

    On the Connection Between Rational Uniform Approximation and Polynomial Lp Approximation of Functions

    Best Chebyshev Approximation by Smooth Functions

    Approximation in the Hardy Space ℋ1 (D) with Respect to the Norm Topology

    Continuous Selections for Metric Projections


Product details

  • No. of pages: 336
  • Language: English
  • Copyright: © Academic Press 1980
  • Published: January 28, 1980
  • Imprint: Academic Press
  • eBook ISBN: 9781483265124

About the Editors

Ronald A. Devore

Karl Scherer

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