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Author: Walter Gautschi Publisher: SIAM ISBN: 1611974305 Category : Science Languages : en Pages : 335
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: Walter Gautschi Publisher: SIAM ISBN: 1611974305 Category : Science Languages : en Pages : 335
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: Wolfgang Schweizer Publisher: Springer Nature ISBN: 3030642321 Category : Science Languages : en Pages : 282
Book Description
This handbook focuses on special functions in physics in the real and complex domain. It covers more than 170 different functions with additional numerical hints for efficient computation, which are useful to anyone who needs to program with other programming languages as well. The book comes with MATLAB-based programs for each of these functions and a detailed html-based documentation. Some of the explained functions are: Gamma and Beta functions; Legendre functions, which are linked to quantum mechanics and electrodynamics; Bessel functions; hypergeometric functions, which play an important role in mathematical physics; orthogonal polynomials, which are largely used in computational physics; and Riemann zeta functions, which play an important role, e.g., in quantum chaos or string theory. The book’s primary audience are scientists, professionals working in research areas of industries, and advanced students in physics, applied mathematics, and engineering.
Author: Walter Gautschi Publisher: OUP Oxford ISBN: 0191545058 Category : Mathematics Languages : en Pages : 312
Book Description
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 to a 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 and discretization 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 chapter deals 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 appended to 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.
Author: Paul Nevai Publisher: Springer Science & Business Media ISBN: 9400905017 Category : Mathematics Languages : en Pages : 472
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: Francisco Marcellàn Publisher: Springer Science & Business Media ISBN: 3540310622 Category : Mathematics Languages : en Pages : 432
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: Eli Levin Publisher: Springer ISBN: 3319729470 Category : Mathematics Languages : en Pages : 170
Book Description
This book establishes bounds and asymptotics under almost minimal conditions on the varying weights, and applies them to universality limits and entropy integrals. Orthogonal polynomials associated with varying weights play a key role in analyzing random matrices and other topics. This book will be of use to a wide community of mathematicians, physicists, and statisticians dealing with techniques of potential theory, orthogonal polynomials, approximation theory, as well as random matrices.
Author: Walter Gautschi Publisher: ISBN: Category : Digital libraries Languages : en Pages : 0
Book Description
"This book provides access to mathematical objects that are of interest in all the sciences and engineering. It provides data object identification numbers where the relevant information (Matlab pieces of software and numerical tables) can be found."--
Author: Walter Gautschi Publisher: SIAM ISBN: 1611975220 Category : Science Languages : en Pages : 60
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: Eli Levin Publisher: Springer Science & Business Media ISBN: 1461302013 Category : Mathematics Languages : en Pages : 472
Book Description
The analysis of orthogonal polynomials associated with general weights has been a major theme in classical analysis this century. In this monograph, the authors define and discuss their classes of weights, state several of their results on Christoffel functions, Bernstein inequalities, restricted range inequalities, and record their bounds on the orthogonal polynomials, as well as their asymptotic results. This book will be of interest to researchers in approximation theory, potential theory, as well as in some branches of engineering.
Author: Walter Gautschi
Author: Walter Gautschi
Author: Wolfgang Schweizer
Author: Walter Gautschi
Author: Paul Nevai
Author: Francisco Marcellàn
Author: Eli Levin
Author: Walter Gautschi
Author: J. Baik
Author: Walter Gautschi 
Author: Eli Levin