Preconditioning techniques for nonsymmetric and indefinite linear systems
نویسندگان
چکیده
منابع مشابه
Preconditioning Highly Indefinite and Nonsymmetric Matrices
Standard preconditioners, like incomplete factorizations, perform well when the coeecient matrix is diagonally dominant, but often fail on general sparse matrices. We experiment with nonsymmetric permutations and scalings aimed at placing large entries on the diagonal in the context of preconditioning for general sparse matrices. We target highly indeenite, nonsymmetric problems which cause dii...
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A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods. 1. Introduction. We describe a method for computing an incomplete factorization of the inverse of a general sparse matrix A 2 IR nn. The resulting...
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Preconditioners are often conceived as approximate inverses. For nonsingular indeenite matrices of saddle-point (or KKT) form, we show how preconditioners incorporating an exact Schur complement lead to preconditioned matrices with exactly two or exactly three distinct eigenvalues. Thus approximations of the Schur complement lead to preconditioners which can be very eeective even though they ar...
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We introduce a novel strategy for constructing symmetric positive definite (SPD) preconditioners for linear systems with symmetric indefinite matrices. The strategy, called absolute value preconditioning, is motivated by the observation that the preconditioned minimal residual method with the inverse of the absolute value of the matrix as a preconditioner converges to the exact solution of the ...
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New convergence intervals of parameters αi are derived and applied for solving the modified linear systems, which enables a better understanding of how parameters should be chosen. The convergence theorem for H-matrix is given. Meanwhile, we discuss the convergence results forM -matrices linear systems and give some new preconditioners. Numerical examples are used to illustrate our results. Key...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1988
ISSN: 0377-0427
DOI: 10.1016/0377-0427(88)90345-7