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Author : Paul F. Byrd
Publisher :
ISBN 13 :
Total Pages : 44 pages
Book Rating : 4.:/5 (31 download)
Download or read book Gauss Quadrature Rules Involving Some Nonclassical Weight Functions written by Paul F. Byrd and published by . This book was released on 1970 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Walter Gautschi
Publisher : SIAM
ISBN 13 : 1611976359
Total Pages : 152 pages
Book Rating : 4.6/5 (119 download)
Download or read book A Software Repository for Gaussian Quadratures and Christoffel Functions written by Walter Gautschi and published by SIAM. This book was released on 2020-10-30 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Narayan Kovvali
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1608457532
Total Pages : 65 pages
Book Rating : 4.6/5 (84 download)
Download or read book Theory and Applications of Gaussian Quadrature Methods written by Narayan Kovvali and published by Morgan & Claypool Publishers. This book was released on 2011 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gaussian quadrature is a powerful technique for numerical integration that falls under the broad category of spectral methods. The purpose of this work is to provide an introduction to the theory and practice of Gaussian quadrature. We study the approximation theory of trigonometric and orthogonal polynomials and related functions, and examine the analytical framework of Gaussian quadrature. We discuss Gaussian quadrature for bandlimited functions, a topic inspired by some recent developments in the analysis of prolate spheroidal wave functions. Algorithms for the computation of the quadrature nodes and weights are described. Several applications of Gaussian quadrature are given, ranging from the evaluation of special functions to pseudospectral methods for solving differential equations. Software realization of select algorithms is provided.
Author : Robert N. Desmarais
Publisher :
ISBN 13 :
Total Pages : 82 pages
Book Rating : 4.:/5 (31 download)
Download or read book Programs for Computing Abscissas and Weights for Classical and Nonclassical Gaussian Quadrature Formulas written by Robert N. Desmarais and published by . This book was released on 1975 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Walter Gautschi
Publisher : SIAM
ISBN 13 : 1611975220
Total Pages : 60 pages
Book Rating : 4.6/5 (119 download)
Download or read book A Software Repository for Orthogonal Polynomials written by Walter Gautschi and published by SIAM. This book was released on 2018 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Software Repository for Orthogonal Polynomials is the first book that provides graphs and references to online datasets that enable the generation of a large number of orthogonal polynomials with classical, quasi-classical, and nonclassical weight functions. Useful numerical tables are also included. The book will be of interest to scientists, engineers, applied mathematicians, and statisticians.
Author :
Publisher :
ISBN 13 :
Total Pages : 542 pages
Book Rating : 4.:/5 (319 download)
Download or read book NASA Technical Note written by and published by . This book was released on 1975 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bernard Shizgal
Publisher : Springer
ISBN 13 : 9401794545
Total Pages : 431 pages
Book Rating : 4.4/5 (17 download)
Download or read book Spectral Methods in Chemistry and Physics written by Bernard Shizgal and published by Springer. This book was released on 2015-01-07 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficients in gases and other gas dynamical problems based on spectral and pseudospectral solutions of the Boltzmann equation. Radiative transfer in astrophysics and atmospheric science, and applications to space physics are discussed. The relaxation of initial non-equilibrium distributions to equilibrium for several different systems is studied with the Boltzmann and Fokker-Planck equations. The eigenvalue spectra of the linear operators in the Boltzmann, Fokker-Planck and Schrödinger equations are studied with spectral and pseudospectral methods based on non-classical orthogonal polynomials. The numerical methods referred to as the Discrete Ordinate Method, Differential Quadrature, the Quadrature Discretization Method, the Discrete Variable Representation, the Lagrange Mesh Method, and others are discussed and compared. MATLAB codes are provided for most of the numerical results reported in the book - see Link under 'Additional Information' on the the right-hand column.
Author :
Publisher :
ISBN 13 :
Total Pages : 744 pages
Book Rating : 4.:/5 (31 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1981 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : United States. Superintendent of Documents
Publisher :
ISBN 13 :
Total Pages : 1504 pages
Book Rating : 4.F/5 ( download)
Download or read book Monthly Catalog of United States Government Publications, Cumulative Index written by United States. Superintendent of Documents and published by . This book was released on 1979 with total page 1504 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : United States. Superintendent of Documents
Publisher :
ISBN 13 :
Total Pages : 1464 pages
Book Rating : 4.:/5 (89 download)
Download or read book Monthly Catalog of United States Government Publications written by United States. Superintendent of Documents and published by . This book was released on 1966 with total page 1464 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul F. Byrd
Publisher : Springer Science & Business Media
ISBN 13 : 3642651380
Total Pages : 376 pages
Book Rating : 4.6/5 (426 download)
Download or read book Handbook of Elliptic Integrals for Engineers and Scientists written by Paul F. Byrd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Engineers and physicists are more and more encountering integrations involving nonelementary integrals and higher transcendental functions. Such integrations frequently involve (not always in immediately re cognizable form) elliptic functions and elliptic integrals. The numerous books written on elliptic integrals, while of great value to the student or mathematician, are not especially suitable for the scientist whose primary objective is the ready evaluation of the integrals that occur in his practical problems. As a result, he may entirely avoid problems which lead to elliptic integrals, or is likely to resort to graphical methods or other means of approximation in dealing with all but the simplest of these integrals. It became apparent in the course of my work in theoretical aero dynamics that there was a need for a handbook embodying in convenient form a comprehensive table of elliptic integrals together with auxiliary formulas and numerical tables of values. Feeling that such a book would save the engineer and physicist much valuable time, I prepared the present volume.
Author :
Publisher :
ISBN 13 :
Total Pages : 1730 pages
Book Rating : 4.3/5 (91 download)
Download or read book Monthly Catalogue, United States Public Documents written by and published by . This book was released on 1970 with total page 1730 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Claude Brezinski
Publisher : Springer Science & Business Media
ISBN 13 : 146147132X
Total Pages : 770 pages
Book Rating : 4.4/5 (614 download)
Download or read book Walter Gautschi, Volume 3 written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2013-10-24 with total page 770 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author : Walter Gautschi
Publisher : Springer Science & Business Media
ISBN 13 : 0817682597
Total Pages : 611 pages
Book Rating : 4.8/5 (176 download)
Download or read book Numerical Analysis written by Walter Gautschi and published by Springer Science & Business Media. This book was released on 2011-12-06 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Claude Brezinski
Publisher : Springer Science & Business Media
ISBN 13 : 1461470498
Total Pages : 921 pages
Book Rating : 4.4/5 (614 download)
Download or read book Walter Gautschi, Volume 2 written by Claude Brezinski and published by Springer Science & Business Media. This book was released on 2013-10-22 with total page 921 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Author :
Publisher :
ISBN 13 :
Total Pages : 300 pages
Book Rating : 4.:/5 (26 download)
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1972 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Walter Gautschi
Publisher : SIAM
ISBN 13 : 1611974305
Total Pages : 335 pages
Book Rating : 4.6/5 (119 download)
Download or read book Orthogonal Polynomials in MATLAB written by Walter Gautschi and published by SIAM. This book was released on 2016-05-23 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Techniques for generating orthogonal polynomials numerically have appeared only recently, within the last 30 or so years.?Orthogonal Polynomials in MATLAB: Exercises and Solutions?describes these techniques and related applications, all supported by MATLAB programs, and presents them in a unique format of exercises and solutions designed by the author to stimulate participation. Important computational problems in the physical sciences are included as models for readers to solve their own problems.?
