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 l2-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 l2-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 l2-NORM SCALING BASED PRECONDITIONER / G., Fasano; Roma, Massimo. - STAMPA. - National Research Center for Ships and Marine Systems - INSEAN Technical Report N. 2007-002:(2007), pp. 1-11.
ON THE ITERATIVE COMPUTATION OF A l2-NORM SCALING BASED PRECONDITIONER
ROMA, Massimo
2007
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 l2-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 l2-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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
