Strong Linearizations of Rational Matrices

DOI10.1137/16M1099510zbMath1431.65039MaRDI QIDQ4556024

A. Amparan, Zaballa, I., S. Marcaida, Froilán M. Dopico

Publication date: 23 November 2018

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

linearizationnonlinear eigenvalue problemrational matrixstrong linearizationminimal polynomial system matrixstrong block minimal bases linearization

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalue problems (93B60) Linearizations (93B18) Minimal systems representations (93B20) Eigenvalues, singular values, and eigenvectors (15A18) Matrices over function rings in one or more variables (15A54) Matrix pencils (15A22)

Related Items (14)

Linearizations of rational matrices from general representations ⋮ Generalized Fiedler pencils with repetition for rational matrix functions ⋮ Strongly Minimal Self-Conjugate Linearizations for Polynomial and Rational Matrices ⋮ Affine spaces of strong linearizations for rational matrices and the recovery of eigenvectors and minimal bases ⋮ Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis ⋮ Structured eigenvalue backward errors for rational matrix functions with symmetry structures ⋮ Structural backward stability in rational eigenvalue problems solved via block Kronecker linearizations ⋮ Block full rank linearizations of rational matrices ⋮ Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems ⋮ Generalized Fiedler Pencils for Rational Matrix Functions ⋮ Recovery of minimal bases and minimal indices of rational matrices from Fiedler-like pencils ⋮ On minimal bases and indices of rational matrices and their linearizations ⋮ Van Dooren's Index Sum Theorem and Rational Matrices with Prescribed Structural Data ⋮ Structured strong linearizations of structured rational matrices

Uses Software

• NLEIGS

Cites Work

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