Orthogonal Polynomials: Computation and Approximation by Walter Gautschi

Orthogonal Polynomials: Computation and Approximation

byWalter Gautschi

Hardcover | January 27, 2005

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This is the first book on constructive methods for, and applications of orthogonal polynomials, and the first available collection of relevant Matlab codes. The book begins with a concise introduction to the theory of polynomials orthogonal on the real line (or a portion thereof), relative toa positive measure of integration. Topics which are particularly relevant to computation are emphasized. The second chapter develops computational methods for generating the coefficients in the basic three-term recurrence relation. The methods are of two kinds: moment-based methods anddiscretization methods. The former are provided with a detailed sensitivity analysis. Other topics addressed concern Cauchy integrals of orthogonal polynomials and their computation, a new discussion of modification algorithms, and the generation of Sobolev orthogonal polynomials. The final chapterdeals with selected applications: the numerical evaluation of integrals, especially by Gauss-type quadrature methods, polynomial least squares approximation, moment-preserving spline approximation, and the summation of slowly convergent series. Detailed historic and bibliographic notes are appendedto each chapter. The book will be of interest not only to mathematicians and numerical analysts, but also to a wide clientele of scientists and engineers who perceive a need for applying orthogonal polynomials.

About The Author

Walter Gautshi is Professor Emeritus at Purdue University, USA.
Numerical Analysis
Numerical Analysis

by Walter Gautschi

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Title:Orthogonal Polynomials: Computation and ApproximationFormat:HardcoverDimensions:312 pages, 9.21 × 6.14 × 0.85 inPublished:January 27, 2005Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198506724

ISBN - 13:9780198506720

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Table of Contents

Basic Theory1.1. Orthogonal polynomials1.2. Properties of orthogonal polynomials1.3. Three-term recurrence relation1.4. Quadrature rules1.5. Classical orthogonal polynomials1.6. Kernal polynomials1.7. Sobolev orthogonal polynomials1.8. Orthogonal polynomials on the semicircle1.9. Notes to chapter 1Computational Methods2.1. Moment-based methods2.2. Discretization methods2.3. Computing Cauchy integrals of orthogonal polynomials2.4. Modification algorithms2.5. Computing Sobolev orthogonal polynomials2.6. Notes to chapter 2Applications3.1. Quadrature3.2. Least squares approximation3.3. Moment-preserving spline approximation3.4. Slowly convergent series3.5. Notes to chapter 3