The algebraic eigenvalue problem
The algebraic eigenvalue problem
Backward error and condition of structured linear systems
SIAM Journal on Matrix Analysis and Applications
Structured Backward Error and Condition of Generalized Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
A Chart of Backward Errors for Singly and Doubly Structured Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
Eigenvalue condition numbers: zero-structured versus traditional
Journal of Computational and Applied Mathematics
Structured Eigenvalue Condition Numbers
SIAM Journal on Matrix Analysis and Applications
Structured Pseudospectra and the Condition of a Nonderogatory Eigenvalue
SIAM Journal on Matrix Analysis and Applications
Structured Pseudospectra for Small Perturbations
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 7.29 |
We continue the study started in [Noschese and Pasquini, Eigenvalue condition numbers: zero-structured versus traditional. J. Comput. Appl. Math. 185 (2006) 174-189] concerning the sensitivity of simple eigenvalues of a matrix A to perturbations in A that belong to a chosen subspace of matrices. In [Noschese and Pasquini, Eigenvalue condition numbers: zero-structured versus traditional. J. Comput. Appl. Math. 185 (2006) 174-189] the zero-structured perturbations have been considered. Here we focus on patterned perturbations, and the cases of the Toeplitz and of the Hankel matrices are investigated in detail. Useful expressions of the absolute patterned condition number of the eigenvalue @l and of the analogue of the matrix yx^H, which leads to the traditional condition number of @l, are given. MATLAB codes are defined to compare traditional, zero-structured and patterned condition numbers. A report on significant numerical tests is included.