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TW 248
G. De Samblanx and A. Bultheel.
Filtering and restarting orthogonal projection method.
Abstract
We consider the class of the Orthogonal Projection Methods (OPM) to solve iteratively large and generalised eigenvalue problems. An OPM is a method that projects a large eigenvalue problem on a smaller subspace. In this subspace, an approximation of the eigenvalue spectrum can be computed from a small eigenvalue problem using a direct method. We show that many iterative eigenvalue solvers, such as the Arnoldi and Davidson method, can be seen as an OPM. We show in the second part of the text how an OPM can be restarted -- implicitly and explicitly. This restart can be combined with an implicit filtering step, even if inaccurate arithmetic is assumed.
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