✦ LIBER ✦

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

✍ Scribed by V Simoncini; M Pennacchio

Publisher: Elsevier Science
Year: 2004
Tongue: English
Weight: 316 KB
Volume: 380
Category: Article
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(03)00487-7

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✦ Synopsis

We analyze the behavior of Krylov subspace methods for the solution of the symmetric system Mx = (Mγ I )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.