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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| 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 |
