The Mathematical Institute, University of Oxford, Eprints Archive

Computing eigenvalues of real symmetric matrices
with rational filters in real arithmetic

Austin, Anthony P. and Trefethen, Lloyd N. (2015) Computing eigenvalues of real symmetric matrices
with rational filters in real arithmetic.
Technical Report. Unspecified. (Submitted)

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Abstract

Powerful algorithms have recently been proposed for computing eigenvalues of large matrices by methods related to contour integrals; best known are the works of Sakurai and coauthors and Polizzi and coauthors. Even if the matrices are real symmetric, most such methods rely on complex arithmetic, leading to expensive linear systems to solve. An appealing technique for overcoming this starts from the observation that certain discretized contour integrals are equivalent to rational interpolation problems, for which there is no need to leave the real axis. Investigation shows that using rational interpolation per se suffers from instability; however, related techniques involving real rational filters can be very effective. This article presents a technique of this kind that is related to previous work published in Japanese by Murakami.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1883
Deposited By: Helen Taylor
Deposited On:27 May 2015 08:14
Last Modified:29 May 2015 19:34

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