Van Dooren's Index Sum Theorem and Rational Matrices with Prescribed Structural Data
From MaRDI portal
Publication:5232114
DOI10.1137/18M1171370zbMath1428.15016OpenAlexW2802450691MaRDI QIDQ5232114
R. Hollister, Froilán M. Dopico, Luis Miguel Anguas, D. Steven Mackey
Publication date: 29 August 2019
Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/18m1171370
Eigenvalue problems (93B60) Pole and zero placement problems (93B55) Inverse problems in linear algebra (15A29) Numerical solutions to inverse eigenvalue problems (65F18)
Related Items (2)
Strongly Minimal Self-Conjugate Linearizations for Polynomial and Rational Matrices ⋮ On minimal bases and indices of rational matrices and their linearizations
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On matrix polynomials with the same finite and infinite elementary divisors
- Stratification of full rank polynomial matrices
- Spectral equivalence of matrix polynomials and the index sum theorem
- Structured strong linearizations from Fiedler pencils with repetition. I.
- Recovery of eigenvectors of rational matrix functions from Fiedler-like linearizations
- Column reduction of polynomial matrices
- Methods and algorithms of solving spectral problems for polynomial and rational matrices
- Block Kronecker linearizations of matrix polynomials and their backward errors
- The eigenstructure of an arbitrary polynomial matrix: Computational aspects
- Perturbation theory for homogeneous polynomial eigenvalue problems
- Backward error and condition of polynomial eigenvalue problems
- Robustness and perturbations of minimal bases
- Möbius transformations of matrix polynomials
- Generic complete eigenstructures for sets of matrix polynomials with bounded rank and degree
- Triangularizing matrix polynomials
- Stability Analysis of the Two-level Orthogonal Arnoldi Procedure
- Linearizations for Rational Matrix Functions and Rosenbrock System Polynomials
- Triangularizing Quadratic Matrix Polynomials
- On the Inverse Symmetric Quadratic Eigenvalue Problem
- A Backward Stable Algorithm for Quadratic Eigenvalue Problems
- Chebyshev rootfinding via computing eigenvalues of colleague matrices: when is it stable?
- Solving Rational Eigenvalue Problems via Linearization
- A compact rational Krylov method for large‐scale rational eigenvalue problems
- An algorithm for the complete solution of quadratic eigenvalue problems
- Minimal Bases of Rational Vector Spaces, with Applications to Multivariable Linear Systems
- Finite and infinite structures of rational matrices: a local approach
- Properties of the system matrix of a generalized state-space system†
- Strong Linearizations of Rational Matrices
- The nonlinear eigenvalue problem
- Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
- NLEIGS: A Class of Fully Rational Krylov Methods for Nonlinear Eigenvalue Problems
- Matrix Polynomials with Completely Prescribed Eigenstructure
- Compact Rational Krylov Methods for Nonlinear Eigenvalue Problems
- Locating the Eigenvalues of Matrix Polynomials
- Vector Spaces of Linearizations for Matrix Polynomials
- Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
- Approximation of Large-Scale Dynamical Systems
This page was built for publication: Van Dooren's Index Sum Theorem and Rational Matrices with Prescribed Structural Data