A method for computing a few eigenpairs of large generalized eigenvalue problems

DOI10.1016/j.apnum.2022.08.018zbMath1505.65169OpenAlexW4293474932MaRDI QIDQ2085682

Qiang Ye, Maged Alkilayh, Lothar Reichel

Publication date: 18 October 2022

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2022.08.018

zbMATH Keywords

generalized eigenvalue problemlarge-scale problemgeneralized Krylov subspace method

Mathematics Subject Classification ID

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

Uses Software

• EIGIFP
• MatrixMarket

Cites Work

• Tikhonov regularization based on generalized Krylov subspace methods
• Efficient determination of the hyperparameter in regularized total least squares problems
• A fast algorithm for solving regularized total least squares problems
• Tikhonov regularization via flexible Arnoldi reduction
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• A refined shift-and-invert Arnoldi algorithm for large unsymmetric generalized eigenproblems.
• An Arnoldi method for nonlinear eigenvalue problems
• Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems
• A survey on variational characterizations for nonlinear eigenvalue problems
• Perturbation analysis for palindromic and anti-palindromic nonlinear eigenvalue problems
• Krylov type subspace methods for matrix polynomials
• Numerical Methods for Large Eigenvalue Problems
• Accelerating the LSTRS Algorithm
• Numerical methods for large eigenvalue problems
• The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
• A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
• IRBL: An Implicitly Restarted Block-Lanczos Method for Large-Scale Hermitian Eigenproblems
• A Krylov Subspace Method for Quadratic Matrix Polynomials with Application to Constrained Least Squares Problems
• An Inverse Free Preconditioned Krylov Subspace Method for Symmetric Generalized Eigenvalue Problems
• Preconditioned gradient iterations for the eigenproblem of definite matrix pairs

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