Quantitative Approximation
Proceedings of a Symposium on Quantitative Approximation Held in Bonn, West Germany, August 20-24, 1979
- 1st Edition - January 28, 1980
- Latest edition
- Editors: Ronald A. Devore, Karl Scherer
- Language: English
Quantitative Approximation provides information pertinent to nonlinear approximation, including rational approximation and optimal knot spline approximation. This book discusses… Read more
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Description
Description
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
Table of contents
Contributors
Preface
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
Problems
Product details
Product details
- Edition: 1
- Latest edition
- Published: May 10, 2014
- Language: English
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