Structured strong $\boldsymbol{\ell}$-ifications for structured matrix polynomials in the monomial basis

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Canonical forms, reductions, classification (15A21) Matrix pencils (15A22) Matrix exponential and similar functions of matrices (15A16)

Uses Software

NLEVP

Cites Work

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On a class of matrix pencils and $\ell$-ifications equivalent to a given matrix polynomial
Spectral equivalence of matrix polynomials and the index sum theorem
Structured strong linearizations from Fiedler pencils with repetition. I.
Fiedler companion linearizations for rectangular matrix polynomials
Palindromic quadratization and structure-preserving algorithm for palindromic matrix polynomials of even degree
Palindromic companion forms for matrix polynomials of odd degree
A permuted factors approach for the linearization of polynomial matrices
A real-coninvolutory analog of the polar decomposition
Companion matrix patterns
Structured strong linearizations from Fiedler pencils with repetition. II
Polynomial zigzag matrices, dual minimal bases, and the realization of completely singular polynomials
Pentadiagonal companion matrices
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
Möbius transformations of matrix polynomials
A note on generalized companion pencils in the monomial basis
Structure preserving deflation of infinite eigenvalues in structured pencils
On vector spaces of linearizations for matrix polynomials in orthogonal bases
The Quadratic Eigenvalue Problem
Fiedler-comrade and Fiedler--Chebyshev pencils
Backward errors for eigenvalues and eigenvectors of Hermitian, skew-Hermitian,H-even andH-odd matrix polynomials
Structured Eigenvalue Backward Errors of Matrix Pencils and Polynomials with Hermitian and Related Structures
Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form
Fiedler Companion Linearizations and the Recovery of Minimal Indices
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
NLEVP
Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
Linearization of matrix polynomials expressed in polynomial bases
Structured backward error analysis of linearized structured polynomial eigenvalue problems
Explicit block-structures for block-symmetric Fiedler-like pencils
A new family of companion forms of polynomial matrices
Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
Matrix Polynomials with Completely Prescribed Eigenstructure
A Framework for Structured Linearizations of Matrix Polynomials in Various Bases
Constructing Strong Linearizations of Matrix Polynomials Expressed in Chebyshev Bases
Eigenvectors and minimal bases for some families of Fiedler-like linearizations
Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
Linearizations of polynomial matrices with symmetries and their applications
Linear Perturbation Theory for Structured Matrix Pencils Arising in Control Theory
Constructing strong $\ell$-ifications from dual minimal bases

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