Fast computation of eigenvalues of companion, comrade, and related matrices

DOI10.1007/s10543-013-0449-xzbMath1293.65052OpenAlexW2025783125MaRDI QIDQ2450887

Raf Vandebril, Jared Lee Aurentz, David S. Watkins

Publication date: 23 May 2014

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-013-0449-x

zbMATH Keywords

eigenvaluenumerical examplesrecurrence relationNewton iterationcompanion matrixpolynomial rootcomrade matrix\(LR\) algorithm\(LR\) factorization

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical computation of roots of polynomial equations (65H04)

Related Items (8)

On the factorization and the inverse of a tridiagonal matrix ⋮ Accurate quadrature of nearly singular line integrals in two and three dimensions by singularity swapping ⋮ Fast and Backward Stable Computation of Roots of Polynomials, Part II: Backward Error Analysis; Companion Matrix and Companion Pencil ⋮ Pentadiagonal companion matrices ⋮ Factorization of Hessenberg matrices ⋮ On the stability of computing polynomial roots via confederate linearizations ⋮ A CMV-Based Eigensolver for Companion Matrices ⋮ Fast and Backward Stable Computation of Roots of Polynomials

Cites Work

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• Francis’s Algorithm
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• The QR Transformation A Unitary Analogue to the LR Transformation--Part 1
• Fast Computation of the Zeros of a Polynomial via Factorization of the Companion Matrix
• Differential qd Algorithm with Shifts for Rank-Structured Matrices
• Fast QR Eigenvalue Algorithms for Hessenberg Matrices Which Are Rank‐One Perturbations of Unitary Matrices
• The Matrix Eigenvalue Problem

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