Condition numbers for inversion of Fiedler companion matrices

DOI10.1016/j.laa.2012.09.020zbMath1281.15004OpenAlexW2072207498MaRDI QIDQ389559

Froilán M. Dopico, Fernando De Terán, Javier J. Pérez

Publication date: 21 January 2014

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

Full work available at URL: https://doi.org/10.1016/j.laa.2012.09.020

zbMATH Keywords

polynomialssingular valuescondition numbersFiedler companion matricesFrobenius companion matricesinverse of Fiedler companion matricesstaircase matrices

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Numerical computation of matrix norms, conditioning, scaling (65F35) Conditioning of matrices (15A12) Special matrices (15B99)

Related Items (10)

Block Kronecker linearizations of matrix polynomials and their backward errors ⋮ Linearizations of matrix polynomials in Bernstein bases ⋮ Linearizations of matrix polynomials in Newton bases ⋮ Polynomial zigzag matrices, dual minimal bases, and the realization of completely singular polynomials ⋮ Pentadiagonal companion matrices ⋮ New bounds for roots of polynomials based on Fiedler companion matrices ⋮ Factoring Block Fiedler Companion Matrices ⋮ Bilinear characterizations of companion matrices ⋮ Companion matrix patterns ⋮ Backward error and conditioning of Fiedler companion linearizations

Uses Software

• Matlab

Cites Work

• Fiedler companion linearizations for rectangular matrix polynomials
• Palindromic companion forms for matrix polynomials of odd degree
• A permuted factors approach for the linearization of polynomial matrices
• Controllability and stability radii for companion form systems
• A note on companion matrices
• Fiedler Companion Linearizations and the Recovery of Minimal Indices
• Recovery of Eigenvectors and Minimal Bases of Matrix Polynomials from Generalized Fiedler Linearizations
• Matrix Analysis
• A new family of companion forms of polynomial matrices
• Unnamed Item

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