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BIT Numerical Mathematics

Erschienen in:

01.09.2016

Generalized averaged Gauss quadrature rules for the approximation of matrix functionals

verfasst von: Lothar Reichel, Miodrag M. Spalević, Tunan Tang

Erschienen in: BIT Numerical Mathematics | Ausgabe 3/2016

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Abstract

The need to compute expressions of the form \(u^*f(A)v\), where A is a large square matrix, u and v are vectors, and f is a function, arises in many applications, including network analysis, quantum chromodynamics, and the solution of linear discrete ill-posed problems. Commonly used approaches first reduce A to a small matrix by a few steps of the Hermitian or non-Hermitian Lanczos processes and then evaluate the reduced problem. This paper describes a new method to determine error estimates for computed quantities and shows how to achieve higher accuracy than available methods for essentially the same computational effort. Our methods are based on recently proposed generalized averaged Gauss quadrature formulas.

Vorheriger Artikel Reconstruction of sparse Legendre and Gegenbauer expansions

Nächster Artikel Analysis and computation of a nonlinear Korteweg-de Vries system

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The requirements on the bounds of the spectrum of A can be weakened depending on the location of the node \(\zeta \).

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Titel: Generalized averaged Gauss quadrature rules for the approximation of matrix functionals
verfasst von: Lothar Reichel
Miodrag M. Spalević
Tunan Tang
Publikationsdatum: 01.09.2016
Verlag: Springer Netherlands
Erschienen in: BIT Numerical Mathematics / Ausgabe 3/2016
Print ISSN: 0006-3835
Elektronische ISSN: 1572-9125
DOI: https://doi.org/10.1007/s10543-015-0592-7

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