Istituto di Matematica Applicata e Tecnologie Informatiche     
Simoncini V., Pennacchio M. The behavior of symmetric Krylov subspace solvers on matrix--dependent right-hand side. Technical report ercim.cnr.ian//2001-1225, 2001.
We analyze the behavior of Krylov subspace methods for the solution of the symmetric system $M x = (M-gamma I)v$ when $gamma$ 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 explicit new relations are provided. Numerical experiments are also included.
Subject Symmetric linear systems. Iterative methods. Krylov subspace methods.

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