Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Structured Pseudospectra for Polynomial Eigenvalue Problems, with Applications
SIAM Journal on Matrix Analysis and Applications
Existence, Uniqueness, and Parametrization of Lagrangian Invariant Subspaces
SIAM Journal on Matrix Analysis and Applications
Condition Number and Backward Error for the Generalized Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
The Conditioning of Linearizations of Matrix Polynomials
SIAM Journal on Matrix Analysis and Applications
Structured Polynomial Eigenvalue Problems: Good Vibrations from Good Linearizations
SIAM Journal on Matrix Analysis and Applications
Backward Error of Polynomial Eigenproblems Solved by Linearization
SIAM Journal on Matrix Analysis and Applications
Structured Hölder Condition Numbers for Multiple Eigenvalues
SIAM Journal on Matrix Analysis and Applications
Structured Backward Errors and Pseudospectra of Structured Matrix Pencils
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 0.00 |
Necessary and sufficient conditions are obtained for simple eigenvalues of complex matrix polynomials with $\star$-even/odd and $\star$-palindromic/antipalindromic structures to have the same normwise condition number with respect to structure preserving and arbitrary perturbations. Here, $\star$ denotes either the transpose $T$ or the conjugate transpose $*$. Exact expressions for the normwise structured condition number of simple eigenvalues of $*$-palindromic/antipalindromic and $T$-even/odd polynomials and tight bounds that localize the structured condition number of simple eigenvalues of $T$-palindromic/antipalindromic and $*$-even/odd polynomials are also obtained. The backward error of complex numbers $z$ as approximate eigenvalues of these polynomials is also considered, and necessary and sufficient conditions are obtained for a given complex number $z$ to have the same structured and unstructured backward errors.