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.

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:

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:

Download or read book Quadrature Formulae written by Aldo Ghizzetti and published by . This book was released on 1970 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Gaussian Quadrature Formulas written by Frank Bowman and published by . This book was released on 1966 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Gaussian Quadrature Formulas written by A. H. Stroud and published by . This book was released on 1966 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Tables of Gaussian Quadrature Formulas written by R. Piessens and published by . This book was released on 1975 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Download or read book Gaussian Quadrature Formulas in Extended Precision written by Richard Michael Silla and published by . This book was released on 1984 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Student s Guide to Bayesian Statistics written by Ben Lambert and published by SAGE. This book was released on 2018-04-20 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics. Without sacrificing technical integrity for the sake of simplicity, the author draws upon accessible, student-friendly language to provide approachable instruction perfectly aimed at statistics and Bayesian newcomers. Through a logical structure that introduces and builds upon key concepts in a gradual way and slowly acclimatizes students to using R and Stan software, the book covers: An introduction to probability and Bayesian inference Understanding Bayes′ rule Nuts and bolts of Bayesian analytic methods Computational Bayes and real-world Bayesian analysis Regression analysis and hierarchical methods This unique guide will help students develop the statistical confidence and skills to put the Bayesian formula into practice, from the basic concepts of statistical inference to complex applications of analyses.

Download or read book Handbook of Mathematical Functions written by Milton Abramowitz and published by Courier Corporation. This book was released on 1965-01-01 with total page 1068 pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive summary of mathematical functions that occur in physical and engineering problems

Download or read book Error Estimates for Gaussian Quadrature Formulas and Applications written by Tsann-Hoa Charles Chen and published by . This book was released on 1980 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Orthogonal Rational Functions written by Adhemar Bultheel and published by Cambridge University Press. This book was released on 1999-02-13 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book generalises the classical theory of orthogonal polynomials on the complex unit circle, or on the real line to orthogonal rational functions whose poles are among a prescribed set of complex numbers. The first part treats the case where these poles are all outside the unit disk or in the lower half plane. Classical topics such as recurrence relations, numerical quadrature, interpolation properties, Favard theorems, convergence, asymptotics, and moment problems are generalised and treated in detail. The same topics are discussed for the different situation where the poles are located on the unit circle or on the extended real line. In the last chapter, several applications are mentioned including linear prediction, Pisarenko modelling, lossless inverse scattering, and network synthesis. This theory has many applications in theoretical real and complex analysis, approximation theory, numerical analysis, system theory, and in electrical engineering.

Download or read book Nodes and Weights of Quadrature Formulas written by Aleksandr S. Konrod and published by Springer. This book was released on 1965-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Table of the Zeros of the Legendre Polynomials of Order 1 16 written by Arnold Noah Lowan and published by . This book was released on 1942 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book E B Christoffel the Influence of His Work on Mathematics and the Physical Sciences written by Paul Leo Butzer and published by . This book was released on 1981 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quadpack written by R. Piessens and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 1. Overview of Numerical Quadrature The numerical evaluation of integrals is one of the oldest problems in mathematics. One can trace its roots back at least to Archimedes. The task is to compute the value of the definite integral of a given function. This is the area under a curve in one dimension or a volume in several dimensions. In addition to being a problem of great practi cal interest it has also lead to the development of mathematics of much beauty and insight. Many portions of approximation theory are directly applicable to integration and results from areas as diverse as orthogo nal polynomials, Fourier series and number theory have had important implications for the evaluation of integrals. We denote the problem addressed here as numerical integration or numerical quadrature. Over the years analysts and engineers have contributed to a growing body of theorems, algorithms and lately, programs, for the solution of this specific problem. Much effort has been devoted to techniques for the analytic evalua tion of integrals. However, most routine integrals in practical scien tific work are incapable of being evaluated in closed form. Even if an expression can be derived for the value of an integral, often this reveals itself only after inordinate amounts of error prone algebraic manipulation. Recently some computer procedures have been developed which can perform analytic integration when it is possible.