Quantitative Approximation - 1st Edition - ISBN: 9780122136504, 9781483265124

Quantitative Approximation

1st Edition

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

Editors: Ronald A. Devore Karl Scherer
eBook ISBN: 9781483265124
Imprint: Academic Press
Published Date: 28th January 1980
Page Count: 336
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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



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



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© Academic Press 1980
Academic Press
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About the Editor

Ronald A. Devore

Karl Scherer

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