A Software Repository for Orthogonal Polynomials PDF Download

Author: Walter Gautschi
Publisher: SIAM
ISBN: 1611975220
Category : Science
Languages : en
Pages : 60

View

Book Description
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: Walter Gautschi
Publisher: SIAM
ISBN: 1611976359
Category : Mathematics
Languages : en
Pages : 152

View

Book Description
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: Kyle Novak
Publisher: Equal Share Press
ISBN:
Category : Mathematics
Languages : en
Pages : 710

View

Book Description
A comprehensive guide to the theory, intuition, and application of numerical methods in linear algebra, analysis, and differential equations. With extensive commentary and code for three essential scientific computing languages: Julia, Python, and Matlab.

Author: Michael T. Heath
Publisher: SIAM
ISBN: 1611975573
Category : Science
Languages : en
Pages : 567

View

Book Description
This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it continues to be used in the classroom. This Classics edition has been updated to include pointers to Python software and the Chebfun package, expansions on barycentric formulation for Lagrange polynomial interpretation and stochastic methods, and the availability of about 100 interactive educational modules that dynamically illustrate the concepts and algorithms in the book. Scientific Computing: An Introductory Survey, Second Edition is intended as both a textbook and a reference for computationally oriented disciplines that need to solve mathematical problems.

Author: Francisco Marcellàn
Publisher: Springer Science & Business Media
ISBN: 3540310622
Category : Mathematics
Languages : en
Pages : 432

View

Book Description
Special functions and orthogonal polynomials in particular have been around for centuries. Can you imagine mathematics without trigonometric functions, the exponential function or polynomials? In the twentieth century the emphasis was on special functions satisfying linear differential equations, but this has now been extended to difference equations, partial differential equations and non-linear differential equations. The present set of lecture notes containes seven chapters about the current state of orthogonal polynomials and special functions and gives a view on open problems and future directions. The topics are: computational methods and software for quadrature and approximation, equilibrium problems in logarithmic potential theory, discrete orthogonal polynomials and convergence of Krylov subspace methods in numerical linear algebra, orthogonal rational functions and matrix orthogonal rational functions, orthogonal polynomials in several variables (Jack polynomials) and separation of variables, a classification of finite families of orthogonal polynomials in Askey’s scheme using Leonard pairs, and non-linear special functions associated with the Painlevé equations.

Author: Walter Gautschi
Publisher: SIAM
ISBN: 1611974305
Category : Science
Languages : en
Pages : 335

View

Book Description
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.?

Author: Theodore S Chihara
Publisher: Courier Corporation
ISBN: 0486141411
Category : Mathematics
Languages : en
Pages : 276

View

Book Description
Assuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. Numerous examples and exercises, an extensive bibliography, and a table of recurrence formulas supplement the text.

Author: Herbert Stahl
Publisher: Cambridge University Press
ISBN: 9780521415347
Category : Mathematics
Languages : en
Pages : 272

View

Book Description
An encyclopedic presentation of general orthogonal polynomials, placing emphasis on asymptotic behaviour and zero distribution.

Author: Paul Nevai
Publisher: Springer Science & Business Media
ISBN: 9400905017
Category : Mathematics
Languages : en
Pages : 472

View

Book Description
This volume contains the Proceedings of the NATO Advanced Study Institute on "Orthogonal Polynomials and Their Applications" held at The Ohio State University in Columbus, Ohio, U.S.A. between May 22,1989 and June 3,1989. The Advanced Study Institute primarily concentrated on those aspects of the theory and practice of orthogonal polynomials which surfaced in the past decade when the theory of orthogonal polynomials started to experience an unparalleled growth. This progress started with Richard Askey's Regional Confer ence Lectures on "Orthogonal Polynomials and Special Functions" in 1975, and subsequent discoveries led to a substantial revaluation of one's perceptions as to the nature of orthogonal polynomials and their applicability. The recent popularity of orthogonal polynomials is only partially due to Louis de Branges's solution of the Bieberbach conjecture which uses an inequality of Askey and Gasper on Jacobi polynomials. The main reason lies in their wide applicability in areas such as Pade approximations, continued fractions, Tauberian theorems, numerical analysis, probability theory, mathematical statistics, scattering theory, nuclear physics, solid state physics, digital signal processing, electrical engineering, theoretical chemistry and so forth. This was emphasized and convincingly demonstrated during the presentations by both the principal speakers and the invited special lecturers. The main subjects of our Advanced Study Institute included complex orthogonal polynomials, signal processing, the recursion method, combinatorial interpretations of orthogonal polynomials, computational problems, potential theory, Pade approximations, Julia sets, special functions, quantum groups, weighted approximations, orthogonal polynomials associated with root systems, matrix orthogonal polynomials, operator theory and group representations.

Author: Gabor Szegš
Publisher: American Mathematical Soc.
ISBN: 0821810235
Category : Mathematics
Languages : en
Pages : 432

View

Book Description
The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.