A Software Repository for Gaussian Quadratures and Christoffel Functions
A Software Repository for Gaussian Quadratures and Christoffel Functions

Author: Walter Gautschi

Publisher: SIAM

Published: 2020-10-30

Total Pages: 153

ISBN-13: 1611976359

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This companion piece to the author’s 2018 book, A Software Repository for Orthogonal Polynomials, focuses on Gaussian quadrature and the related Christoffel function. The book makes Gauss quadrature rules of any order easily accessible for a large variety of weight functions and for arbitrary precision. It also documents and illustrates known as well as original approximations for Gauss quadrature weights and Christoffel functions. The repository contains 60+ datasets, each dealing with a particular weight function. Included are classical, quasi-classical, and, most of all, nonclassical weight functions and associated orthogonal polynomials. Scientists, engineers, applied mathematicians, and statisticians will find the book of interest.

Numerical Analysis
Numerical Analysis

Author: Walter Gautschi

Publisher: Springer Science & Business Media

Published: 2011-12-06

Total Pages: 611

ISBN-13: 0817682597

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Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.

Christofell, E. B.
Christofell, E. B.

Author: Elwin Bruno Christoffel

Publisher: Birkhäuser

Published: 1981

Total Pages: 798

ISBN-13:

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This memorial volume is dedicated to E. B. Christoffel on the occasion of the 150th anniversary of his birth. Its aim is, on the one hand, to present the life of Christoffel and the scientific milieu in which he worked and, on the other hand, to present a survey of his work not only in its historical context but especially in the frame of contemporary mathematics and physics. For one thing, this book contains expanded versions of the twelve invited lectures given at the International Christoffel Symposium, held on November 8- 11, 1979 at Aachen and Monschau. For another, the scope of these papers has been broadened by soliciting some fourty-five additional invited articles, concerned either with further aspects of the work of Christoffel or with specia lized topics in fields in which Christoffel had worked. This should give the reader a greater opportunity to appreciate the richness of Christoffel's contributions to the mathematical and physical sciences, and not only its immediate impact but also its subsequent infiuence. It can be discerned that Christoffel did basic work not only in differential geometry or, better still, in classical tensor analysis, thereby supplying the mathematical foundations of Einstein's theory of general relativity, but also in a variety of other areas of mathematics. The scope of Christoffel's work can be appreciated from the following synopsis of the thirteen chapters into which the festschrift is divided. Chap."

Walter Gautschi, Volume 2
Walter Gautschi, Volume 2

Author: Claude Brezinski

Publisher: Springer Science & Business Media

Published: 2013-10-22

Total Pages: 921

ISBN-13: 1461470498

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Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi’s most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter’s prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1 Numerical Conditioning Special Functions Interpolation and Approximation Selected Works with Commentaries, Vol. 2 Orthogonal Polynomials on the Real Line Orthogonal Polynomials on the Semicircle Chebyshev Quadrature Kronrod and Other Quadratures Gauss-type Quadrature Selected Works with Commentaries, Vol. 3 Linear Difference Equations Ordinary Differential Equations Software History and Biography Miscellanea Works of Werner Gautschi