In this paper we consider the Krylov subspace based method introduced in [Fasano, 2005a], for iteratively solving the symmetric and possibly indefinite linear system Ax = b. We emphasize the application of the latter method to compute a diagonal preconditioner. The approach proposed is based on the approximate computation of the `2-norm of the rows (columns) of the matrix A and on its use to equilibrate the matrix A. The distinguishing feature of this approach is that the computation of the `2-norm is performed without requiring the knowledge of the entries of the matrix A but only using a routine which provides the product of A times a vector.

On the iterative computation of a l_2-norm scaling based preconditioner

FASANO, Giovanni;
2007-01-01

Abstract

In this paper we consider the Krylov subspace based method introduced in [Fasano, 2005a], for iteratively solving the symmetric and possibly indefinite linear system Ax = b. We emphasize the application of the latter method to compute a diagonal preconditioner. The approach proposed is based on the approximate computation of the `2-norm of the rows (columns) of the matrix A and on its use to equilibrate the matrix A. The distinguishing feature of this approach is that the computation of the `2-norm is performed without requiring the knowledge of the entries of the matrix A but only using a routine which provides the product of A times a vector.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10278/15016
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