A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems (Q1855433)
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scientific article; zbMATH DE number 1864792
| Language | Label | Description | Also known as |
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| English | A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems |
scientific article; zbMATH DE number 1864792 |
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A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems (English)
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5 February 2003
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This paper is a follow-up to two papers by the second author [ibid. 322, 61--85, 87--104 (2001; Zbl 0976.65034, Zbl 0976.65035)]. There a simple preconditioned eigensolver for the computation of the smallest eigenvalue and associated eigenvector of a positive definite matrix was studied and an estimate for its convergence rate was given. In this paper a much shorter and more elegant convergence rate estimate is given. Moreover it is shwon that this estimate holds also for the generalized symmetric eigenvalue problem.
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conjugate gradient method
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preconditioning
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eigenvalue
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eigenvector
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positive definite matrix
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convergence
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generalized symmetric eigenvalue problem
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