A Framework for Structured Linearizations of Matrix Polynomials in Various Bases

DOI10.1137/16M106296XzbMath1365.15028arXiv1603.05773MaRDI QIDQ5346749

Leonardo Robol, Paul Van Dooren, Raf Vandebril

Publication date: 29 May 2017

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

Full work available at URL: https://arxiv.org/abs/1603.05773

zbMATH Keywords

rational functionsmatrix polynomialsdual minimal basesstrong linearizationspalindromic matrix polynomialsnonmonomial baseseven matrix polynomials

Mathematics Subject Classification ID

Matrices over function rings in one or more variables (15A54) Matrix pencils (15A22)

Related Items (21)

Block Kronecker linearizations of matrix polynomials and their backward errors ⋮ Block minimal bases \(\ell\)-ifications of matrix polynomials ⋮ Linearizations of rational matrices from general representations ⋮ Strong Linearizations of Rational Matrices ⋮ Structured strong $\boldsymbol{\ell}$-ifications for structured matrix polynomials in the monomial basis ⋮ On vector spaces of linearizations for matrix polynomials in orthogonal bases ⋮ Linearizations of matrix polynomials in Newton bases ⋮ Unnamed Item ⋮ Uniform Determinantal Representations ⋮ Generalized Standard Triples for Algebraic Linearizations of Matrix Polynomials ⋮ The infinite Lanczos method for symmetric nonlinear eigenvalue problems ⋮ Structured backward error analysis of linearized structured polynomial eigenvalue problems ⋮ Algebraic linearizations of matrix polynomials ⋮ Factoring Block Fiedler Companion Matrices ⋮ A Class of Quasi-Sparse Companion Pencils ⋮ A simplified approach to Fiedler-like pencils via block minimal bases pencils ⋮ Robustness and perturbations of minimal bases. II: The case with given row degrees ⋮ Robustness and perturbations of minimal bases ⋮ Efficient Ehrlich-Aberth iteration for finding intersections of interpolating polynomials and rational functions ⋮ Compact Two-Sided Krylov Methods for Nonlinear Eigenvalue Problems ⋮ Explicit block-structures for block-symmetric Fiedler-like pencils

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