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Block Kronecker linearizations of matrix polynomials and their backward errors (Q1616007)

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Language	Label	Description	Also known as
English	Block Kronecker linearizations of matrix polynomials and their backward errors	scientific article

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scholarly article

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Block Kronecker linearizations of matrix polynomials and their backward errors (English)

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Froilán M. Dopico

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Piers W. Lawrence

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Javier J. Pérez

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Paul Van Dooren

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Numerische Mathematik

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publication date

31 October 2018

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full work available at URL

https://arxiv.org/abs/1707.04843

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describes a project that uses

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MaRDI profile type

MaRDI publication profile

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Linearization of matrix polynomials expressed in polynomial bases

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A new family of companion forms of polynomial matrices

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A Pencil Approach for Embedding a Polynomial Matrix into a Unimodular matrix

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Chapter 1: DAEs, Control, and Optimization

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

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Structured strong linearizations from Fiedler pencils with repetition. I.

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Recovery of Eigenvectors and Minimal Bases of Matrix Polynomials from Generalized Fiedler Linearizations

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

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A simplified approach to Fiedler-like pencils via block minimal bases pencils

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Palindromic linearizations of a matrix polynomial of odd degreee obtained from Fiedler pencils with repetition

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Sharp lower bounds for the dimension of linearizations of matrix polynomials

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Fiedler Companion Linearizations and the Recovery of Minimal Indices

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Palindromic companion forms for matrix polynomials of odd degree

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Fiedler companion linearizations for rectangular matrix polynomials

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Spectral equivalence of matrix polynomials and the index sum theorem

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Polynomial zigzag matrices, dual minimal bases, and the realization of completely singular polynomials

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Condition numbers for inversion of Fiedler companion matrices

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Backward stability of polynomial root-finding using Fiedler companion matrices

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Matrix Polynomials with Completely Prescribed Eigenstructure

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Constructing strong \(\ell\)-ifications from dual minimal bases

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The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part I

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The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part II

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Pentadiagonal companion matrices

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A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part I: Versal Deformations

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A Geometric Approach to Perturbation Theory of Matrices and Matrix Pencils. Part II: A Stratification-Enhanced Staircase Algorithm

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Polynomial Roots from Companion Matrix Eigenvalues

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A note on companion matrices

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Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems

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General theory of regular matrix polynomials and band Toeplitz operators

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THE COLLEAGUE MATRIX, A CHEBYSHEV ANALOGUE OF THE COMPANION MATRIX

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The nonlinear eigenvalue problem

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An algorithm for the complete solution of quadratic eigenvalue problems

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Backward Error of Polynomial Eigenproblems Solved by Linearization

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Symmetric Linearizations for Matrix Polynomials

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The Conditioning of Linearizations of Matrix Polynomials

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Stratification of full rank polynomial matrices

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Eigenvalues of tridiagonal pseudo-Toeplitz matrices

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Stability of rootfinding for barycentric Lagrange interpolants

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Backward Error of Polynomial Eigenvalue Problems Solved by Linearization of Lagrange Interpolants

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Constructing Strong Linearizations of Matrix Polynomials Expressed in Chebyshev Bases

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Backward Error Analysis of Polynomial Eigenvalue Problems Solved by Linearization

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Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations

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Vector Spaces of Linearizations for Matrix Polynomials

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Möbius transformations of matrix polynomials

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Exact and Approximate Modeling of Linear Systems

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The autonomous linear quadratic control problem. Theory and numerical solution

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Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods

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On the stability of computing polynomial roots via confederate linearizations

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Vector Spaces of Linearizations for Matrix Polynomials: A Bivariate Polynomial Approach

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Fiedler-comrade and Fiedler--Chebyshev pencils

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Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable?

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A Framework for Structured Linearizations of Matrix Polynomials in Various Bases

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On the Sensitivity of the Eigenvalue Problem $Ax = \lambda Bx$

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Backward error and condition of polynomial eigenvalue problems

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The Quadratic Eigenvalue Problem

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The computation of Kronecker's canonical form of a singular pencil

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The generalized eigenstructure problem in linear system theory

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Deadbeat control: A special inverse eigenvalue problem

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The eigenstructure of an arbitrary polynomial matrix: Computational aspects

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Robustness and perturbations of minimal bases

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The ubiquitous Kronecker product

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A permuted factors approach for the linearization of polynomial matrices

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A Backward Stable Algorithm for Quadratic Eigenvalue Problems

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Identifiers

zbMATH Open document ID

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10.1007/s00211-018-0969-z

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:1616007

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