The behavior of symmetric Krylov subspace methods for solving Mx=( M− γI) v

We analyze the behavior of Krylov subspace methods for the solution of the symmetric system Mx=( M− γI) v when γ is close to some of the extreme eigenvalues of M. We show that a stagnation phase may occur if the structure of the right-hand side is not taken into account, and we analyze the occurrenc...

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Bibliographic Details
Published in:Linear algebra and its applications 2004-03, Vol.380, p.53-71
Main Authors: Simoncini, V, Pennacchio, M
Format: Article
Language:English
Subjects:
Iterative methods
Krylov subspace methods
Symmetric linear systems
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Summary:We analyze the behavior of Krylov subspace methods for the solution of the symmetric system Mx=( M− γI) v when γ is close to some of the extreme eigenvalues of M. We show that a stagnation phase may occur if the structure of the right-hand side is not taken into account, and we analyze the occurrence and persistence of such stagnation. A natural alternative strategy is proposed and we show that the new approach provides a better approximation, with the same number of matrix–vector multiplications. Numerical experiments are also included.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(03)00487-7