Name
Title | ||
|---|---|---|
Extended and Improved Criss-Cross Algorithms for Computing the Spectral Value Set Abscissa and Radius. |
Abstract | ||
|---|---|---|
In this paper, we extend the original criss-cross algorithms for computing the epsilon-pseudospectral abscissa and radius to general spectral value sets. By proposing new root-finding-based strategies for the horizontal/radial search subphases, we significantly reduce the number of expensive Hamiltonian eigenvalue decompositions incurred, which typically translates to meaningful speedups in overall computation times. Furthermore, and partly necessitated by our root-finding approach, we develop a new way of handling the singular pencils or problematic interior searches that can arise when computing the epsilon-spectral value set radius. Compared to would-be direct extensions of the original algorithms, that is, without our additional modifications, our improved criss-cross algorithms are not only noticeably faster but also more robust and numerically accurate, for both spectral value set and pseudospectral problems. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1137/19M1246213 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
pseudospectra,robust stability,stability radius,Hamiltonian,symplectic,H-infinity norm | Value set,Hamiltonian (quantum mechanics),Abscissa,Algorithm,Mathematics,Eigenvalues and eigenvectors,Special case | Journal |
Volume | Issue | ISSN |
40 | 4 | 0895-4798 |
Citations | PageRank | References |
0 | 0.34 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peter Benner | 1 | 825 | 114.06 |
| Tim Mitchell | 2 | 6 | 1.19 |