Title: Implicitly restarted Arnoldi with purification for the shift-invert transformation
Authors: Meerbergen, Karl ×
Spence, A #
Issue Date: Apr-1997
Publisher: Amer mathematical soc
Series Title: Mathematics of computation vol:66 issue:218 pages:667-689
Abstract: The need to determine a few eigenvalues of a large sparse generalised eigenvalue problem Ax = lambda Bx with positive semidefinite B arises in many physical situations, for example, in a stability analysis of the discretised Navier-Stokes equation. A common technique is to apply Arnoldi's method to the shift-invert transformation, but this can suffer fr um numerical instabilities as is illustrated by a numerical example. In this paper, a new method that avoids instabilities is presented which is based on applying the implicitly restarted Arnoldi method with the B semi-inner product and a purification step. The paper contains a rounding error analysis and ends with brief comments on some extensions.
ISSN: 0025-5718
Publication status: published
KU Leuven publication type: IT
Appears in Collections:NUMA, Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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