Implicit QR for companion-like pencils

DOI10.1090/mcom/3020zbMath1335.65041arXiv1401.5606OpenAlexW1782979359MaRDI QIDQ2796017

Paola Boito, Luca Gemignani, Yu.S.Eidel'man

Publication date: 23 March 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.5606

zbMATH Keywords

eigenvaluenumerical experimentsmatrix pencilsunitary matricesQZ algorithmimplicit QR algorithmlow rank corrections

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Matrix pencils (15A22)

Related Items

Time and space efficient generators for quasiseparable matrices ⋮ Fast and Backward Stable Computation of Roots of Polynomials, Part II: Backward Error Analysis; Companion Matrix and Companion Pencil ⋮ A real QZ algorithm for structured companion pencils ⋮ Structured generalized eigenvalue condition numbers for parameterized quasiseparable matrices ⋮ On the stability of computing polynomial roots via confederate linearizations ⋮ A CMV-Based Eigensolver for Companion Matrices ⋮ Accurate Computation of Generalized Eigenvalues of Regular SR-BP Pairs

Uses Software

• Polynomial Toolbox

Cites Work

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• On the fast reduction of a quasiseparable matrix to Hessenberg and tridiagonal forms
• Completing a matrix when certain entries of its inverse are specified
• On a new class of structured matrices
• Pseudozeros of polynomials and pseudospectra of companion matrices
• The eigenstructure of an arbitrary polynomial matrix: Computational aspects
• Separable type representations of matrices and fast algorithms. Volume 1. Basics. Completion problems. Multiplication and inversion algorithms
• Separable type representations of matrices and fast algorithms. Volume 2. Eigenvalue method
• Efficient eigenvalue computation for quasiseparable Hermitian matrices under low rank perturbations
• Leverrier's algorithm for singular systems
• A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations
• Solving Polynomials with Small Leading Coefficients
• Polynomial Roots from Companion Matrix Eigenvalues
• Balancing Regular Matrix Pencils
• Roots of Polynomials Expressed in Terms of Orthogonal Polynomials
• ON MATRICES DEPENDING ON PARAMETERS

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