Name
Abstract | ||
|---|---|---|
In many applications it is important to understand the sensitivity of eigenvalues of a matrix polynomial to perturbations of the polynomial. The sensitivity commonly is described by condition numbers or pseudospectra. However, the determination of pseudospectra of matrix polynomials is very demanding computationally. This paper describes a new approach to computing approximations of pseudospectra of matrix polynomials by using rank-one or projected rank-one perturbations. These perturbations are inspired by Wilkinson’s analysis of eigenvalue sensitivity. This approach allows the approximation of both structured and unstructured pseudospectra. Computed examples show the method to perform much better than a method based on random rank-one perturbations both for the approximation of structured and unstructured (i.e., standard) polynomial pseudospectra. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.cam.2018.09.033 | Journal of Computational and Applied Mathematics |
Keywords | Field | DocType |
Matrix polynomials,Pseudospectrum,Structured pseudospectrum,Eigenvalue sensitivity,Distance from defectivity,Numerical methods | Mathematical optimization,Pseudospectrum,Polynomial,Matrix (mathematics),Approximations of π,Matrix polynomial,Eigenvalues and eigenvectors,Perturbation (astronomy),Mathematics,Computation | Journal |
Volume | ISSN | Citations |
350 | 0377-0427 | 0 |
PageRank | References | Authors |
0.34 | 12 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Silvia Noschese | 1 | 32 | 6.77 |
| Lothar Reichel | 2 | 453 | 95.02 |