On validity of m-step multisplitting preconditioners for linear systems

摘要

Let Ax=b be a linear system where A is a symmetric positive definite (spd) matrix. m-step multisplitting preconditioners, which include the preconditioners based on multisplittings obtained by incomplete Cholesky factorizations [R. Bru, C. Corral, A. Martínez, J. Mas, SIAM J. Matrix Anal. Appl. 16 (1995) 1210–1222], for the conjugate gradient method are studied. The validity of the proposed m-step multisplitting preconditioners when A is an spd matrix is proved. Our results improve and extend previous ones.