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Theory and Applications of Gaussian Quadrature Methods [electronic resource] / by Narayan Kovvali.

By: Kovvali, Narayan [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthesis Lectures on Algorithms and Software in Engineering: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2011Edition: 1st ed. 2011.Description: VIII, 57 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783031015175.Subject(s): Signal processing | Signal, Speech and Image ProcessingAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 621,382 Online resources: Click here to access online
Contents:
Introduction -- Approximating with Polynomials and Related Functions -- Gaussian Quadrature -- Applications -- Links to Mathematical Software.
In: Springer Nature eBookSummary: 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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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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