EAN: 9783031003899

SYNTHESIS LECTURES ON ALGORITHMS AND SOFTWARE I...

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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