We present a technique for building effective and low cost preconditioners for sequences of shifted linear systems (A + αI) x_α = b, where A is symmetric positive definite and α > 0. This technique updates a preconditioner for A, available in the form of an LDL^T factorization, by modifying only the nonzero entries of the L factor in such a way that the resulting preconditioner mimics the diagonal of the shifted matrix and reproduces its overall behavior. This approach is supported by a theoretical analysis as well as by numerical experiments, showing that it works efficiently for a broad range of values of α.
Efficient preconditioner updates for shifted linear systems / Bellavia, S.; De Simone, V.; Di Serafino, D.; Morini, B.. - In: SIAM JOURNAL ON SCIENTIFIC COMPUTING. - ISSN 1064-8275. - 33:4(2011), pp. 1785-1809. [10.1137/100803419]
Efficient preconditioner updates for shifted linear systems
Di Serafino D.
;
2011
Abstract
We present a technique for building effective and low cost preconditioners for sequences of shifted linear systems (A + αI) x_α = b, where A is symmetric positive definite and α > 0. This technique updates a preconditioner for A, available in the form of an LDL^T factorization, by modifying only the nonzero entries of the L factor in such a way that the resulting preconditioner mimics the diagonal of the shifted matrix and reproduces its overall behavior. This approach is supported by a theoretical analysis as well as by numerical experiments, showing that it works efficiently for a broad range of values of α.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
