The theory and the practice of optimal preconditioning in solving a linear system by iterative processes is founded on some theoretical facts understandable in terms of a class V of spaces of matrices including diagonal algebras and group matrix algebras. The V-structure lets us extend some known crucial results of preconditioning theory and obtain some useful information on the computability and on the efficiency of new preconditioners. Three preconditioners not yet considered in literature, belonging to three corresponding algebras of V, are analyzed in detail. Some experimental results are included.
DI FIORE, C., Zellini, P. (2001). Matrix algebras in optimal preconditioning. LINEAR ALGEBRA AND ITS APPLICATIONS, 335, 1-54 [10.1016/S0024-3795(00)00137-3].
Matrix algebras in optimal preconditioning
DI FIORE, CARMINE;ZELLINI, PAOLO
2001-01-01
Abstract
The theory and the practice of optimal preconditioning in solving a linear system by iterative processes is founded on some theoretical facts understandable in terms of a class V of spaces of matrices including diagonal algebras and group matrix algebras. The V-structure lets us extend some known crucial results of preconditioning theory and obtain some useful information on the computability and on the efficiency of new preconditioners. Three preconditioners not yet considered in literature, belonging to three corresponding algebras of V, are analyzed in detail. Some experimental results are included.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
