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- W2021378499 abstract "We consider the class of the Orthogonal Projection Methods (OPM) to solve iteratively large 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. Examples of OPMs are the Arnoldi and the Davidson method. We show how an OPM can be restarted — implicitly and explicitly. This restart can be used to remove a specific subset of vectors from the approximation subspace. This is called explicit filtering. An implicit restart can also be combined with an implicit filtering step, i.e. the application of a polynomial or rational function on the subspace, even if inaccurate arithmetic is assumed. However, the condition for the implicit application of a filter is that the rank of the residual matrix must be small." @default.
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- W2021378499 date "1999-01-01" @default.
- W2021378499 modified "2023-09-28" @default.
- W2021378499 title "Restrictions on implicit filtering techniques for orthogonal projection methods" @default.
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- W2021378499 doi "https://doi.org/10.1016/s0024-3795(98)10153-2" @default.
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