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Matrices, moments, and rational quadrature

Please always quote using this URN:urn:nbn:de:0296-matheon-3836
  • Many problems in science and engineering require the evaluation of functionals of the form $F(A) = u^T f(A)u$, where $A$ is a large symmetric matrix, $u$ a vector, and $f$ a nonlinear function. A popular and fairly inexpensive approach to determining upper and lower bounds for such functionals is based on first carrying out a few steps of the Lanczos procedure applied to $A$ with initial vector $u$, and then evaluating pairs of Gauss and Gauss-Radau quadrature rules associated with the tridiagonal matrix determined by the Lanczos procedure. The present paper extends this approach to allow the use of rational Gauss quadrature rules.

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Metadaten
Author:Guillermo López Lagomasino, Lothar Reichel, Lena Wunderlich
URN:urn:nbn:de:0296-matheon-3836
Referee:Volker Mehrmann
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/01/23
Release Date:2009/01/22
Institute:Technische Universität Berlin
Preprint Number:542
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