Theory and Applications of Gaussian Quadrature Methods / by Narayan Kovvali.

Format:

Book

Author/Creator:

Kovvali, Narayan., Author.

Series:

Synthesis Lectures on Algorithms and Software in Engineering, 1938-1735

Language:

English

Subjects (All):

Signal processing.

Signal, Speech and Image Processing .

Local Subjects:

Signal, Speech and Image Processing .

Physical Description:

1 online resource (VIII, 57 p.)

Edition:

1st ed. 2011.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2011.

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.

Contents:

Introduction

Approximating with Polynomials and Related Functions

Gaussian Quadrature

Applications

Links to Mathematical Software.

ISBN:

9783031015175

3031015177