Twice Is Enough for Dangerous Eigenvalues

DOI10.1137/20M1385330zbMath1482.65058arXiv2010.09710OpenAlexW4205614778MaRDI QIDQ5028553

Yuji Nakatsukasa, Andrew Horning

Publication date: 10 February 2022

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.09710

zbMATH Keywords

Arnoldi methodsubspace iterationrational filters

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Roundoff error (65G50)

Uses Software

• FEAST
• mctoolbox
• Eigtool

Cites Work

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• The behavior of eigenvalues and singular values under perturbations of restricted rank
• A projection method for generalized eigenvalue problems using numerical integration.
• Matrix Algorithms
• Introduction to Perturbation Methods
• FEAST As A Subspace Iteration Eigensolver Accelerated By Approximate Spectral Projection
• Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver
• Numerical Methods for Large Eigenvalue Problems
• Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
• Numerical Methods for Computing Angles Between Linear Subspaces
• Accuracy and Stability of Numerical Algorithms
• FEAST for Differential Eigenvalue Problems
• Computing Eigenvalues of Real Symmetric Matrices with Rational Filters in Real Arithmetic
• Angles between subspaces and their tangents

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