Short-Term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices
نویسندگان
چکیده
منابع مشابه
Short-Term Recurrence Krylov Subspace Methods for Nearly Hermitian Matrices
The Progressive GMRES algorithm, introduced by Beckermann and Reichel in 2008, is a residual-minimizing short-recurrence Krylov subspace method for solving a linear system in which the coefficient matrix has a low-rank skew-Hermitian part. We analyze this algorithm, observing a critical instability that makes the method unsuitable for some problems. To work around this issue we introduce a diff...
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Abstract. It is well known that generalized conjugate gradient (cg) methods, fulfilling a minimization property in the whole spanned Krylov space, cannot be formulated with short recurrences for nonsymmetric system matrices. Here, Krylov subspace methods are proposed that do fulfill a minimization property and can be implemented as short recurrence method at the same time. These properties are ...
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Incomplete LDL∗ factorizations sometimes produce an inde nite preconditioner even when the input matrix is Hermitian positive de nite. The two most popular iterative solvers for Hermitian systems, MINRES and CG, cannot use such preconditioners; they require a positive de nite preconditioner. We present two new Krylov-subspace solvers, a variant of MINRES and a variant of CG, both of which can b...
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It is well known that the projection of a matrix A onto a Krylov subspace span { h, Ah, Ah, . . . , Ak−1h } results in a matrix of Hessenberg form. We show that the projection of the same matrix A onto an extended Krylov subspace, which is of the form span { A−krh, . . . , A−2h, A−1h,h, Ah, Ah . . . , A`h } , is a matrix of so-called extended Hessenberg form which can be characterized uniquely ...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2012
ISSN: 0895-4798,1095-7162
DOI: 10.1137/110851006