Large vector spaces of block-symmetric strong linearizations of matrix polynomials

DOI10.1016/j.laa.2015.03.032zbMath1312.65052OpenAlexW1994574097MaRDI QIDQ2341908

Yanyan Li

Publication date: 6 May 2015

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

Full work available at URL: https://doi.org/10.1016/j.laa.2015.03.032

zbMATH Keywords

matrix polynomialsstructured matrix polynomialsFiedler pencils with repetitiongeneralized Fiedler pencils with repetitionstrong linearizationsblock-symmetric linearizationsvector space \(\mathbb{DL}(P)\)

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) 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 ⋮ A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error ⋮ Block minimal bases \(\ell\)-ifications of matrix polynomials ⋮ On vector spaces of linearizations for matrix polynomials in orthogonal bases ⋮ Counting Fiedler pencils with repetitions ⋮ Linearizations of Hermitian Matrix Polynomials Preserving the Sign Characteristic ⋮ Constructing Strong Linearizations of Matrix Polynomials Expressed in Chebyshev Bases ⋮ Automatic recovery of eigenvectors and minimal bases of matrix polynomials from generalized Fiedler pencils with repetition ⋮ Structured backward error analysis of linearized structured polynomial eigenvalue problems ⋮ Factoring Block Fiedler Companion Matrices ⋮ A Class of Quasi-Sparse Companion Pencils ⋮ A simplified approach to Fiedler-like pencils via block minimal bases pencils ⋮ On the sign characteristic of Hermitian linearizations in \(\mathbb{DL}(P)\) ⋮ Block Kronecker ansatz spaces for matrix polynomials ⋮ Palindromic linearizations of palindromic matrix polynomials of odd degree obtained from Fiedler-like pencils ⋮ On minimal bases and indices of rational matrices and their linearizations ⋮ Explicit block-structures for block-symmetric Fiedler-like pencils ⋮ Fiedler-comrade and Fiedler--Chebyshev pencils ⋮ Inertia laws and localization of real eigenvalues for generalized indefinite eigenvalue problems ⋮ Structured strong linearizations of structured rational matrices ⋮ Constructing symmetric structure-preserving strong linearizations

Cites Work

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• Skew-symmetric matrix polynomials and their Smith forms
• Spectral equivalence of matrix polynomials and the index sum theorem
• Structured strong linearizations from Fiedler pencils with repetition. I.
• Hermitian matrix polynomials with real eigenvalues of definite type. I: Classification
• Palindromic companion forms for matrix polynomials of odd degree
• A permuted factors approach for the linearization of polynomial matrices
• Structured strong linearizations from Fiedler pencils with repetition. II
• The computation of Kronecker's canonical form of a singular pencil
• Jordan structures of alternating matrix polynomials
• General theory of regular matrix polynomials and band Toeplitz operators
• Fast projection methods for minimal design problems in linear system theory
• Polynomial eigenvalue problems with Hamiltonian structure
• Backward error and condition of polynomial eigenvalue problems
• The Quadratic Eigenvalue Problem
• Smith forms of palindromic matrix polynomials
• Recovery of Eigenvectors and Minimal Bases of Matrix Polynomials from Generalized Fiedler Linearizations
• Palindromic linearizations of a matrix polynomial of odd degreee obtained from Fiedler pencils with repetition
• Definite Matrix Polynomials and their Linearization by Definite Pencils
• A new family of companion forms of polynomial matrices
• Linearizations of Hermitian Matrix Polynomials Preserving the Sign Characteristic
• Vector Spaces of Linearizations for Matrix Polynomials
• Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
• Symmetric Linearizations for Matrix Polynomials
• Linearizations of polynomial matrices with symmetries and their applications

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