Restarted GMRES is known to be inefficient for solving shifted systems when the shifts are handled simultaneously. Variants have been proposed to enhance its performance. We show that another restarted method, restarted Full Orthogonalization Method (FOM), can effectively be employed. The total number of iterations of restarted FOM applied to all shifted systems simultaneously is the same as that obtained by applying restarted FOM to the shifted system with slowest convergence rate, while the computational cost grows only sub-linearly with the number of shifts. Numerical experiments are reported.
Simoncini, V. (2003). Restarted full orthogonalization method for shifted linear systems. BIT, 43(2), 459-466 [10.1023/A:1026000105893].
Restarted full orthogonalization method for shifted linear systems
Simoncini V.
2003
Abstract
Restarted GMRES is known to be inefficient for solving shifted systems when the shifts are handled simultaneously. Variants have been proposed to enhance its performance. We show that another restarted method, restarted Full Orthogonalization Method (FOM), can effectively be employed. The total number of iterations of restarted FOM applied to all shifted systems simultaneously is the same as that obtained by applying restarted FOM to the shifted system with slowest convergence rate, while the computational cost grows only sub-linearly with the number of shifts. Numerical experiments are reported.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
