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Theory and Applications of Gaussian Quadrature Methods / by Narayan Kovvali

By: Kovvali, Narayan V. S. K., autor
Material type: materialTypeLabelE-bookSeries: (Synthesis Lectures on Algorithms and Software in Engineering, 1938-1735).Publisher: Cham : Springer International Publishing, 2011Edition: 1st edition 2011.Description: 1 recurso en línea (VIII, 57 páginas).ISBN: 9783031015175.Subject: Análisis numérico | Aproximación, Teoría de laOnline resources: Acceso a este recurso digital (usuarios Universidad Europea de Madrid)Digital Resources
Contents:
Introduction -- Approximating with Polynomials and Related Functions -- Gaussian Quadrature -- Applications -- Links to Mathematical Software.
Summary: 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.
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Holdings
Item type Current library Collection Call number Status Date due Barcode Item holds
LIBRO-E NO PRÉSTAMO LIBRO-E NO PRÉSTAMO Madrid Digital Acceso Electrónico (UEM) Ciencias e Ingeniería QA299.4.G3 2011 EB (Browse shelf(Opens below)) Acceso electrónico eBook.01112236
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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.

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