Combination preconditioning and self-adjointness in non-standard inner products with application to saddle point problems
نویسندگان
چکیده
It is widely appreciated that the iterative solution of linear systems of equations with large sparse matrices is much easier when the matrix is symmetric. It is equally advantageous to employ symmetric iterative methods when a nonsymmetric matrix is self-adjoint in a non-standard inner product. Here, general conditions for such self-adjointness are considered. In particular, a number of known examples for saddle point systems are surveyed and combined to make new combination preconditioners which are self-adjoint in different inner products.
منابع مشابه
Combination preconditioning of saddle point systems for positive definiteness
Amongst recent contributions to preconditioning methods for saddle point systems, standard iterative methods in nonstandard inner products have been usefully employed. Krzyżanowski (Numer. Linear Algebra Appl. 2011; 18:123–140) identified a two-parameter family of preconditioners in this context and Stoll and Wathen (SIAM J. Matrix Anal. Appl. 2008; 30:582–608) introduced combination preconditi...
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