Pentadiagonal companion matrices

DOI10.1515/spma-2016-0003zbMath1338.15074OpenAlexW2325676038MaRDI QIDQ908193

Kevin N. Vander Meulen, Brydon Eastman

Publication date: 3 February 2016

Published in: Special Matrices (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/spma-2016-0003

zbMATH Keywords

algorithmszeros of polynomialspentadiagonal matricesFiedler companion matricescompanion matricesHessenberg matrices

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Factorization of matrices (15A23) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Eigenvalues, singular values, and eigenvectors (15A18) Special matrices (15B99)

Related Items (5)

Block Kronecker linearizations of matrix polynomials and their backward errors ⋮ Structured strong $\boldsymbol{\ell}$-ifications for structured matrix polynomials in the monomial basis ⋮ A Class of Quasi-Sparse Companion Pencils ⋮ A note on generalized companion pencils in the monomial basis ⋮ Non-sparse Companion Matrices

Cites Work

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• Characterization of a family of generalized companion matrices
• Condition numbers for inversion of Fiedler companion matrices
• A quasiseparable approach to five-diagonal CMV and Fiedler matrices
• A permuted factors approach for the linearization of polynomial matrices
• Companion matrix patterns
• A fast implicit QR eigenvalue algorithm for companion matrices
• A note on companion matrices
• On the shifted QR iteration applied to companion matrices
• Extremal sparsity of the companion matrix of a polynomial
• Fast computation of eigenvalues of companion, comrade, and related matrices
• Fiedler Companion Linearizations and the Recovery of Minimal Indices
• Fast Computation of the Zeros of a Polynomial via Factorization of the Companion Matrix
• Symmetric Linearizations for Matrix Polynomials
• A CMV-Based Eigensolver for Companion Matrices

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