Composite orthogonal projection methods for large matrix eigenproblems

DOI10.1007/BF02880075zbMath0958.65040OpenAlexW2024312641MaRDI QIDQ1585577

Zhongxiao Jia

Publication date: 16 November 2000

Published in: Science in China. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02880075

zbMATH Keywords

convergenceeigenvalue problemeigenvectorserror boundsorthogonal basesRitz methodArnoldi algorithmrefined projection

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Ill-posedness and regularization problems in numerical linear algebra (65F22)

Related Items

The distance of an eigenvector to a Krylov subspace and the convergence of the Arnoldi method for eigenvalue problems, On perturbation bounds for orthogonal projections, A refined shift-and-invert Arnoldi algorithm for large unsymmetric generalized eigenproblems., A refined Jacobi-Davidson method and its correction equation, A dynamic thick restarted semi-refined ABLE algorithm for computing a few selected eigentriplets of large nonsymmetric matrices, Residuals of refined projection methods for large matrix eigenproblems, Using cross-product matrices to compute the SVD, On the perturbation of an \(L^2\)-orthogonal projection, Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm, The refined harmonic Arnoldi method and an implicitly restarted refined algorithm for computing interior eigenpairs of large matrices, Orthogonal projection method for eigenpair derivatives of large symmetric matrices, A refined harmonic Rayleigh-Ritz procedure and an explicitly restarted refined harmonic Arnoldi algorithm

Uses Software

• JDQZ

Cites Work

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• Computing interior eigenvalues of large matrices
• Generalized block Lanczos methods for large unsymmetric eigenproblems
• Refined iterative algorithms based on Arnoldi's process for large unsymmetric eigenproblems
• A refined iterative algorithm based on the block Arnoldi process for large unsymmetric eigenproblems
• The Convergence of Generalized Lanczos Methods for Large Unsymmetric Eigenproblems
• Approximate solutions and eigenvalue bounds from Krylov subspaces
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• The principle of minimized iterations in the solution of the matrix eigenvalue problem