Name
Abstract | ||
|---|---|---|
This work considers eigenvalue problems that are nonlinear in the eigenvalue parameter. Given such a nonlinear eigenvalue problem T, we are concerned with finding the minimal backward error such that T has a set of prescribed eigenvalues with prescribed algebraic multiplicities. We consider backward errors that only allow constant perturbations, which do not depend on the eigenvalue parameter. While the usual resolvent norm addresses this question for a single eigenvalue of multiplicity one, the general setting involving several eigenvalues is significantly more difficult. Under mild assumptions, we derive a singular value optimization characterization for the minimal perturbation that addresses the general case. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/130927462 | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
nonlinear eigenvalue problem,analytic matrix-valued function,Sylvester-like operator,backward error | Mathematical optimization,Nonlinear system,Algebraic number,Singular value,Eigenvalue perturbation,Mathematical analysis,Resolvent,Divide-and-conquer eigenvalue algorithm,Mathematics,Eigenvalues and eigenvectors,Inverse iteration | Journal |
Volume | Issue | ISSN |
35 | 3 | 0895-4798 |
Citations | PageRank | References |
0 | 0.34 | 10 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Karow | 1 | 68 | 9.25 |
| Daniel Kressner | 2 | 449 | 48.01 |
| Emre Mengi | 3 | 8 | 4.82 |