A geometric theory for preconditioned inverse iteration applied to a subspace
نویسندگان
چکیده
منابع مشابه
A geometric theory for preconditioned inverse iteration applied to a subspace
The aim of this paper is to provide a convergence analysis for a preconditioned subspace iteration, which is designated to determine a modest number of the smallest eigenvalues and its corresponding invariant subspace of eigenvectors of a large, symmetric positive definite matrix. The algorithm is built upon a subspace implementation of preconditioned inverse iteration, i.e., the well-known inv...
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The topic of this paper is a convergence analysis of preconditioned inverse iteration (PINVIT). A sharp estimate for the eigenvalue approximations is derived; the eigenvector approximations are controlled by an upper bound for the residual vector. The analysis is mainly based on extremal properties of various quantities which define the geometry of PINVIT.
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Preconditioned gradient iterations for very large eigenvalue problems are efficient solvers with growing popularity. However, only for the simplest preconditioned eigensolver, namely the preconditioned gradient iteration (or preconditioned inverse iteration) with fixed step size, sharp non-asymptotic convergence estimates are known. These estimates require a properly scaled preconditioner. In t...
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The discretization of eigenvalue problems for partial differential operators is a major source of matrix eigenvalue problems having very large dimensions, but only some of the smallest eigenvalues together with the eigenvectors are to be determined. Preconditioned inverse iteration (a “matrix factorization–free” method) derives from the well–known inverse iteration procedure in such a way that ...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2001
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-01-01357-6