Linearizations for Rational Matrix Functions and Rosenbrock System Polynomials

DOI10.1137/15M1008622zbMath1376.65042OpenAlexW2303035367MaRDI QIDQ2797106

Rafikul Alam, Namita Behera

Publication date: 4 April 2016

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

Full work available at URL: https://doi.org/10.1137/15m1008622

zbMATH Keywords

eigenvaluelinearizationminimal realizationeigenvectorzerosspectrummatrix polynomialmatrix pencilpolesLTI systemFiedler pencilrational matrix function

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57) Numerical computation of matrix norms, conditioning, scaling (65F35)

Related Items (22)

Linearizations of rational matrices from general representations ⋮ Strong Linearizations of Rational Matrices ⋮ Generalized Fiedler pencils with repetition for rational matrix functions ⋮ Automatic recovery of eigenvectors and minimal bases of matrix polynomials from generalized Fiedler pencils with repetition ⋮ 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 ⋮ Fully actuated system approach for linear systems control: a frequency-domain solution ⋮ The nonlinear eigenvalue problem ⋮ 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 ⋮ Recovery of eigenvectors of rational matrix functions from Fiedler-like linearizations ⋮ A spectral Newton-Schur algorithm for the solution of symmetric generalized eigenvalue problems ⋮ On minimal bases and indices of rational matrices and their linearizations ⋮ Cone-constrained rational eigenvalue problems ⋮ Sensitivity Analysis of Nonlinear Eigenproblems ⋮ Van Dooren's Index Sum Theorem and Rational Matrices with Prescribed Structural Data ⋮ Fiedler Linearizations for Higher Order State-Space Systems ⋮ Structured strong linearizations of structured rational matrices

Uses Software

• NLEVP

Cites Work

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• The continuing influence of Fiedler's work on companion matrices
• Spectral equivalence of matrix polynomials and the index sum theorem
• Numerical simulation of three dimensional pyramid quantum dot
• Existence and location of eigenvalues for fluid-solid structures
• Rational Krylov for nonlinear eigenproblems, an iterative projection method.
• Eigenfrequencies of a tube bundle placed in a confined fluid
• A rational spectral problem in fluid-solid vibration
• An Arnoldi method for nonlinear eigenvalue problems
• The eigenstructure of an arbitrary polynomial matrix: Computational aspects
• Preconditioned iterative methods for a class of nonlinear eigenvalue problems
• Iterative projection methods for computing relevant energy states of a quantum dot
• Solving Rational Eigenvalue Problems via Linearization
• Fiedler Companion Linearizations and the Recovery of Minimal Indices
• NLEVP
• Linearization of regular matrix polynomials
• A minimax principle for nonlinear eigenvalue problems with applications to nonoverdamped systems
• The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part I
• The generalized Schur decomposition of an arbitrary pencil A–λB—robust software with error bounds and applications. Part II
• A new family of companion forms of polynomial matrices
• Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
• Vector Spaces of Linearizations for Matrix Polynomials
• Algorithms for the Nonlinear Eigenvalue Problem
• Computational Science - ICCS 2004

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