On exact estimates of the convergence rate of the steepest ascent method in the symmetric eigenvalue problem

DOI10.1016/0024-3795(91)90379-BzbMath0731.65023WikidataQ59695922 ScholiaQ59695922MaRDI QIDQ808168

A. L. Skorokhodov, Andrew V. Knyazev

Publication date: 1991

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

zbMATH Keywords

Rayleigh quotientconvergence ratesymmetric eigenvalue problemnonasymptotic estimatesenergy seminormsteepest ascent method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10)

Related Items

Convergence Analysis of Restarted Krylov Subspace Eigensolvers, Iterative minimization of the Rayleigh quotient by block steepest descent iterations, Global convergence of the restarted Lanczos and Jacobi-Davidson methods for symmetric eigenvalue problems, Sharp Ritz value estimates for restarted Krylov subspace iterations, On convergence of iterative projection methods for symmetric eigenvalue problems, On preconditioned eigensolvers and invert-Lanczos processes, An unconstrained global optimization framework for real symmetric eigenvalue problems, Eigenvectors from eigenvalues: A survey of a basic identity in linear algebra, A geometric theory for preconditioned inverse iteration. I: Extrema of Rayleigh quotient, A geometric theory for preconditioned inverse iteration. III: A short and sharp convergence estimate for generalized eigenvalue problems

Cites Work

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• Sharp a priori error estimates of the Rayleigh-Ritz method without assumptions of fixed sign or compactness
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations