Structured backward error analysis of linearized structured polynomial eigenvalue problems

DOI10.1090/mcom/3360zbMath1408.65015arXiv1612.07011OpenAlexW2566778665MaRDI QIDQ4612565

Paul Van Dooren, Froilán M. Dopico, Javier J. Pérez

Publication date: 31 January 2019

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.07011

zbMATH Keywords

Möbius transformationsstructured matrix polynomialsstructured backward error analysiscomplete polynomial eigenproblemsstructure-preserving linearizations

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) Canonical forms, reductions, classification (15A21) Matrix pencils (15A22)

Related Items

Structured strong $\boldsymbol{\ell}$-ifications for structured matrix polynomials in the monomial basis ⋮ Generic skew-symmetric matrix polynomials with fixed rank and fixed odd grade ⋮ Strongly Minimal Self-Conjugate Linearizations for Polynomial and Rational Matrices ⋮ Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis ⋮ Structural backward stability in rational eigenvalue problems solved via block Kronecker linearizations ⋮ Generic Symmetric Matrix Polynomials with Bounded Rank and Fixed Odd Grade ⋮ A simplified approach to Fiedler-like pencils via block minimal bases pencils ⋮ Palindromic linearizations of palindromic matrix polynomials of odd degree obtained from Fiedler-like pencils ⋮ Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations ⋮ Backward error and conditioning of Fiedler companion linearizations

Uses Software

• PEPACK

Cites Work

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