Sharp Convergence Estimates for the Preconditioned Steepest Descent Method for Hermitian Eigenvalue Problems
The paper is concerned with convergence estimates for the preconditioned steepest descent method for the computation of the smallest eigenvalue of a Hermitian operator. Available estimates are reviewed and new estimates are introduced that improve on the known ones in certain respects. In addition t...
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| Veröffentlicht in: | SIAM journal on numerical analysis 2006-01, Vol.43 (6), p.2668-2689 |
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| container_title | SIAM journal on numerical analysis |
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| creator | Ovtchinnikov, E. E. |
| description | The paper is concerned with convergence estimates for the preconditioned steepest descent method for the computation of the smallest eigenvalue of a Hermitian operator. Available estimates are reviewed and new estimates are introduced that improve on the known ones in certain respects. In addition to the estimates for the error reduction after one iteration, we consider estimates for the so-called asymptotic convergence factor defined as the upper limit of the average error reduction per iteration. The paper focuses on sharp estimates, i.e., those that cannot be improved without using additional information. |
| doi_str_mv | 10.1137/040620643 |
| format | Article |
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E.</creator><creatorcontrib>Ovtchinnikov, E. E.</creatorcontrib><description>The paper is concerned with convergence estimates for the preconditioned steepest descent method for the computation of the smallest eigenvalue of a Hermitian operator. Available estimates are reviewed and new estimates are introduced that improve on the known ones in certain respects. In addition to the estimates for the error reduction after one iteration, we consider estimates for the so-called asymptotic convergence factor defined as the upper limit of the average error reduction per iteration. The paper focuses on sharp estimates, i.e., those that cannot be improved without using additional information.</description><identifier>ISSN: 0036-1429</identifier><identifier>EISSN: 1095-7170</identifier><identifier>DOI: 10.1137/040620643</identifier><identifier>CODEN: SJNAEQ</identifier><language>eng</language><publisher>Philadelphia, PA: Society for Industrial and Applied Mathematics</publisher><subject>Accuracy ; Analytical estimating ; Approximation ; Eigenvalues ; Eigenvectors ; Estimate reliability ; Estimates ; Estimation methods ; Euclidean space ; Exact sciences and technology ; Linear systems ; Mathematics ; Numerical analysis ; Numerical analysis. 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| ispartof | SIAM journal on numerical analysis, 2006-01, Vol.43 (6), p.2668-2689 |
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| source | JSTOR Mathematics and Statistics; SIAM journals (Society for Industrial and Applied Mathematics); JSTOR |
| subjects | Accuracy Analytical estimating Approximation Eigenvalues Eigenvectors Estimate reliability Estimates Estimation methods Euclidean space Exact sciences and technology Linear systems Mathematics Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Partial differential equations, boundary value problems Perceptron convergence procedure Preconditioning Real numbers Sciences and techniques of general use |
| title | Sharp Convergence Estimates for the Preconditioned Steepest Descent Method for Hermitian Eigenvalue Problems |
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