The convergence behavior of Ritz values in the presence of close eigenvalues

DOI10.1016/0024-3795(87)90129-7zbMath0632.65035OpenAlexW1989507268WikidataQ94860519 ScholiaQ94860519MaRDI QIDQ1095582

Henk A. van der Vorst, A. van der Sluis

Publication date: 1987

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

Full work available at URL: https://doi.org/10.1016/0024-3795(87)90129-7

zbMATH Keywords

rate of convergencenumerical experimentRitz valuessuperlinear convergencesymmetric matricesclose eigenvaluesdouble eigenvalueKaniel-Paige-Saad a priori upper boundsRitz polynomials

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18)

Related Items

The rate of convergence of conjugate gradients, On sensitivity of Gauss-Christoffel quadrature, A practical termination criterion for the conjugate gradient method, Conjugate gradient type methods and preconditioning, Spectral analysis of parallel incomplete factorizations with implicit pseudo‐overlap, Peaks, plateaus, numerical instabilities in a Galerkin minimal residual pair of methods for solving \(Ax=b\), An adaptive block Lanczos algorithm, Computing the field of values and pseudospectra using the Lanczos method with continuation, A posteriori superlinear convergence bounds for block conjugate gradient, Accelerating the solution of linear systems appearing in two-phase reservoir simulation by the use of POD-based deflation methods, Sharpness in rates of convergence for the symmetric Lanczos method, Further results on the convergence behavior of conjugate-gradients and Ritz values, Subsampling Algorithms for Semidefinite Programming, Eigenvalue computation in the 20th century, Two-sided and alternating Jacobi-Davidson

Cites Work

• The rate of convergence of conjugate gradients
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• Eigenvalues of perturbed Hermitian matrices
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• On Estimating the Largest Eigenvalue with the Lanczos Algorithm
• Influence of the Eigenvalue Spectrum on the Convergence Rate of the Conjugate Gradient Method
• Estimates for Some Computational Techniques in Linear Algebra
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