A new shift strategy for the implicitly restarted refined harmonic Lanczos method

DOI10.1016/j.cam.2017.12.030zbMath1382.65103OpenAlexW2783746317MaRDI QIDQ1696462

Jiana Meng, Datian Niu, Hong-Ying Li

Publication date: 14 February 2018

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2017.12.030

zbMATH Keywords

algorithmnumerical experimentsimplicit restartharmonic Lanczos methodharmonic Ritz pairinterior eigenpairsnew shiftsrefined harmonic Lanczos methodrefined harmonic Ritz pair

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Uses Software

• eigs
• PROPACK
• IRAM

Cites Work

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• Polynomial characterizations of the approximate eigenvectors by the refined Arnoldi method and an implicitly restarted refined Arnoldi algorithm
• 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 refined harmonic Arnoldi method and an implicitly restarted refined algorithm for computing interior eigenpairs of large matrices
• A refined subspace iteration algorithm for large sparse eigenproblems
• A harmonic restarted Arnoldi algorithm for calculating eigenvalues and determining multiplicity
• Some theoretical comparisons of refined Ritz vectors and Ritz vectors
• An analysis of the Rayleigh--Ritz method for approximating eigenspaces
• Matrix Algorithms
• Numerical Methods for Large Eigenvalue Problems
• The Lanczos Algorithm With Partial Reorthogonalization
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• The Lanczos Algorithm with Selective Orthogonalization
• IRBL: An Implicitly Restarted Block-Lanczos Method for Large-Scale Hermitian Eigenproblems
• The convergence of harmonic Ritz values, harmonic Ritz vectors and refined harmonic Ritz vectors
• Harmonic projection methods for large non-symmetric eigenvalue problems
• The Matrix Eigenvalue Problem

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