کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4639342 1632041 2013 12 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the choice of preconditioner for minimum residual methods for non-Hermitian matrices
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
On the choice of preconditioner for minimum residual methods for non-Hermitian matrices
چکیده انگلیسی

We consider the solution of left preconditioned linear systems P−1Cx=P−1cP−1Cx=P−1c, where P,C∈Cn×nP,C∈Cn×n are non-Hermitian, c∈Cnc∈Cn, and CC, PP, and P−1CP−1C are diagonalisable with spectra symmetric about the real line. We prove that, when PP and CC are self-adjoint with respect to the same Hermitian sesquilinear form, the convergence of a minimum residual method in a particular nonstandard inner product applied to the preconditioned linear system is bounded by a term that depends only on the spectrum of P−1CP−1C. The inner product is related to the spectral decomposition of PP. When PP is self-adjoint with respect to a nearby Hermitian sesquilinear form to CC, the convergence of a minimum residual method in this nonstandard inner product applied to the preconditioned linear system is bounded by a term involving the eigenvalues of P−1CP−1C and a constant factor. The size of this factor is related to the nearness of the Hermitian sesquilinear forms. Numerical experiments indicate that for certain matrices eigenvalue-dependent convergence is observed both for the nonstandard method and for standard GMRES.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational and Applied Mathematics - Volume 249, September 2013, Pages 57–68
نویسندگان
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