Theory and Applications of Gaussian Quadrature Methods
Kovvali, Narayan V. S. K.
Theory and Applications of Gaussian Quadrature Methods by Narayan Kovvali - 1st edition 2011 - 1 recurso en línea (VIII, 57 páginas) - Synthesis Lectures on Algorithms and Software in Engineering 1938-1735 .
Introduction -- Approximating with Polynomials and Related Functions -- Gaussian Quadrature -- Applications -- Links to Mathematical Software.
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. Table of Contents: Introduction / Approximating with Polynomials and Related Functions / Gaussian Quadrature / Applications / Links to Mathematical Software.
9783031015175
10.1007/978-3-031-01517-5 doi
Análisis numérico
Aproximación, Teoría de la
QA299.4.G3 / 2011 EB
Theory and Applications of Gaussian Quadrature Methods by Narayan Kovvali - 1st edition 2011 - 1 recurso en línea (VIII, 57 páginas) - Synthesis Lectures on Algorithms and Software in Engineering 1938-1735 .
Introduction -- Approximating with Polynomials and Related Functions -- Gaussian Quadrature -- Applications -- Links to Mathematical Software.
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. Table of Contents: Introduction / Approximating with Polynomials and Related Functions / Gaussian Quadrature / Applications / Links to Mathematical Software.
9783031015175
10.1007/978-3-031-01517-5 doi
Análisis numérico
Aproximación, Teoría de la
QA299.4.G3 / 2011 EB