Saving flops in LU based shift-and-invert strategy

DOI10.1016/j.cam.2010.04.003zbMath1196.65074OpenAlexW1971025528MaRDI QIDQ989130

Hua Xiang, Laura Grigori, Desire Nuentsa Wakam

Publication date: 27 August 2010

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.2010.04.003

zbMATH Keywords

algorithmeigenvaluenumerical examplesLU factorizationdirect methoddivide and conquershift-and-invert

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Direct numerical methods for linear systems and matrix inversion (65F05)

Uses Software

• PARDISO
• eigs
• JDQR
• JDQZ
• IRAM

Cites Work

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• Rational Krylov sequence methods for eigenvalue computation
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
• Convergence analysis of an inexact truncated RQ-iteration
• Inexact inverse iteration for generalized eigenvalue problems
• Inexact Rayleigh quotient-type methods for eigenvalue computations
• Matrix Algorithms
• Average-Case Stability of Gaussian Elimination
• A Chebyshev–Davidson Algorithm for Large Symmetric Eigenproblems
• The Jacobi-Davidson method
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
• Implicit Application of Polynomial Filters in a k-Step Arnoldi Method
• A Truncated RQ Iteration for Large Scale Eigenvalue Calculations
• The Davidson Method
• Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils
• Templates for the Solution of Algebraic Eigenvalue Problems
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• On Large-Scale Diagonalization Techniques for the Anderson Model of Localization

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