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A course in approximation theory / Ward Cheney, Will Light.

By: Contributor(s): Material type: TextTextSeries: The Brooks/Cole series in advanced mathematicsPublication details: Pacific Grove, Calif. : Brooks/Cole Pub. Co., 1999.Description: 359 p. : illISBN:
  • 9780821887110
Subject(s): DDC classification:
  • 511.4 CHE
LOC classification:
  • QA221 .C44 1999
Contents:
* Introductory discussion of interpolation * Linear interpolation operators * Optimization of the Lagrange operator * Multivariate polynomials * Moving the nodes * Projections * Tensor-product interpolation * The Boolean algebra of projections * The Newton paradigm for interpolation * The Lagrange paradigm for interpolation * Interpolation by translates of a single function * Positive definite functions * Strictly positive definite functions * Completely monotone functions * The Schoenberg interpolation theorem * The Micchelli interpolation theorem * Positive definite functions on spheres * Approximation by positive definite functions * Approximate reconstruction of functions and tomography * Approximation by convolution * The good kernels * Ridge functions * Ridge function approximation via convolutions * Density of ridge functions * Artificial neural networks * Chebyshev centers * Optimal reconstruction of functions * Algorithmic orthogonal projections * Cardinal B-splines and the sinc function * The Golomb-Weinberger theory * Hilbert function spaces and reproducing kernels * Spherical thin-plate splines * Box splines * Wavelets, I * Wavelets, II * Quasi-interpolation * Bibliography * Index * Index of symbols
Summary: This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable. Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions. An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.
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Item type Current library Call number Copy number Status Date due Barcode
Project book Project book CUTN Central Library 511.4 CHE (Browse shelf(Opens below)) Checked out to Renuka Devi V (20019T) 31/01/2024 48866
General Books General Books CUTN Central Library Generalia 511.4 CHE (Browse shelf(Opens below)) 1 Available 11235
General Books General Books CUTN Central Library Generalia 511.4 CHE (Browse shelf(Opens below)) 2 Available 11236

Includes bibliographical references and index.

* Introductory discussion of interpolation
* Linear interpolation operators
* Optimization of the Lagrange operator
* Multivariate polynomials
* Moving the nodes
* Projections
* Tensor-product interpolation
* The Boolean algebra of projections
* The Newton paradigm for interpolation
* The Lagrange paradigm for interpolation
* Interpolation by translates of a single function
* Positive definite functions
* Strictly positive definite functions
* Completely monotone functions
* The Schoenberg interpolation theorem
* The Micchelli interpolation theorem
* Positive definite functions on spheres
* Approximation by positive definite functions
* Approximate reconstruction of functions and tomography
* Approximation by convolution
* The good kernels
* Ridge functions
* Ridge function approximation via convolutions
* Density of ridge functions
* Artificial neural networks
* Chebyshev centers
* Optimal reconstruction of functions
* Algorithmic orthogonal projections
* Cardinal B-splines and the sinc function
* The Golomb-Weinberger theory
* Hilbert function spaces and reproducing kernels
* Spherical thin-plate splines
* Box splines
* Wavelets, I
* Wavelets, II
* Quasi-interpolation
* Bibliography
* Index
* Index of symbols

This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable.

Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions.

An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.

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