On a class of matrix pencils and \(\ell\)-ifications equivalent to a given matrix polynomial

DOI10.1016/j.laa.2015.07.017zbMath1338.65099arXiv1406.1025OpenAlexW2962961128MaRDI QIDQ281981

Leonardo Robol, Dario Andrea Bini

Publication date: 11 May 2016

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.1025

zbMATH Keywords

companion matrixlinearizationsmatrix polynomialsmatrix pencilstropical roots

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Vector spaces, linear dependence, rank, lineability (15A03) Canonical forms, reductions, classification (15A21)

Related Items

Block Kronecker linearizations of matrix polynomials and their backward errors, Block minimal bases \(\ell\)-ifications of matrix polynomials, Strong Linearizations of Rational Matrices, Structured strong $\boldsymbol{\ell}$-ifications for structured matrix polynomials in the monomial basis, Factoring Block Fiedler Companion Matrices, Efficient Reduction of Compressed Unitary Plus Low Rank Matrices to Hessenberg Form, Orthogonal iterations on companion-like pencils, Fast Hessenberg Reduction of Some Rank Structured Matrices

Uses Software

• NLEVP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quasiseparable Hessenberg reduction of real diagonal plus low rank matrices and applications
• Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method
• Spectral equivalence of matrix polynomials and the index sum theorem
• Standard triples of structured matrix polynomials
• Fiedler companion linearizations for rectangular matrix polynomials
• Backward error and condition of polynomial eigenvalue problems
• Solving secular and polynomial equations: a multiprecision algorithm
• Triangularizing matrix polynomials
• The Quadratic Eigenvalue Problem
• Triangularizing Quadratic Matrix Polynomials
• Fiedler Companion Linearizations and the Recovery of Minimal Indices
• NLEVP
• Tropical Scaling of Polynomial Matrices
• Definite Matrix Polynomials and their Linearization by Definite Pencils
• Linearization of matrix polynomials expressed in polynomial bases
• Introduction to Matrix Analytic Methods in Stochastic Modeling
• Locating the Eigenvalues of Matrix Polynomials
• Vector Spaces of Linearizations for Matrix Polynomials
• The Conditioning of Linearizations of Matrix Polynomials
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• Symmetric Linearizations for Matrix Polynomials
• Numerical Methods for Structured Markov Chains
• Error Bounds for Zeros of a Polynomial Based Upon Gerschgorin's Theorems
• Some Modified Matrix Eigenvalue Problems