Gene H. Golub and Gérard Meurant: matrices, moments and quadrature with applications

• ID: 2646, RIV: 10104028
• ISSN: 1615-3375, ISBN: not specified
• source: Foundations of Computational Mathematics
• keywords: moments; quadrature; matrices; orthogonal polynomials; continued fractions; Riemann-Stieltjes integral; Krylov subspace methods
• authors: Zdeněk Strakoš
• authors from KNM: Strakoš Zdeněk

Abstract

This paper was written upon the request of the Journal FoCM for the so-called Featured Review of the book given in the title. It takes the opportunity to look thoroughly at the development of the concepts of interpolatory quadrature and moments in their relationship with continued fractions, orthogonal polynomials, Riemann-Stieltjes representation of operators, Jacobi matrices etc. It was shown how these classical topics of analysis, approximation theory and spectral theory of operators found applications in solving modern computational problems via Krylov subspace methods.