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Spectral deflation in Krylov solvers: A theory of coordinate space based methods
- ETNA
"... Abstract. For the iterative solution of large sparse linear systems we develop a theory for a family of augmented and deflated Krylov space solvers that are coordinate based in the sense that the given problem is transformed into one that is formulated in terms of the coordinates with respect to the ..."
Abstract
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Cited by 4 (1 self)
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when the matrix is non-Hermitian, allow us in the case of an exactly invariant subspace to correctly deflate both the right and the corresponding left (possibly generalized) eigenspaces of the matrix, so that convergence only depends on the non-deflated eigenspaces. The minimality of the residual
THE ARNOLDI EIGENVALUE ITERATION WITH EXACT SHIFTS CAN FAIL
- SIAM J. MATRIX ANAL. APPL. VOL. 31, NO. 1, PP. 1–10
, 2009
"... The restarted Arnoldi algorithm, implemented in the ARPACK software library and MATLAB’s eigs command, is among the most common means of computing select eigenvalues and eigenvectors of a large, sparse matrix. To assist convergence, a starting vector is repeatedly refined via the application of aut ..."
Abstract
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Cited by 8 (2 self)
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the algorithm fails in the strongest possible sense; that is, the polynomial filter used to restart the iteration deflates the eigenspace one is attempting to compute.
