Name
Abstract | ||
|---|---|---|
In this paper, we take a quasi-Newton approach to nonlinear eigenvalue problems (NEPs) of the type M(λ)v = 0, where \(M:\mathbb {C}\rightarrow \mathbb {C}^{n\times n}\) is a holomorphic function. We investigate which types of approximations of the Jacobian matrix lead to competitive algorithms, and provide convergence theory. The convergence analysis is based on theory for quasi-Newton methods and Keldysh’s theorem for NEPs. We derive new algorithms and also show that several well-established methods for NEPs can be interpreted as quasi-Newton methods, and thereby, we provide insight to their convergence behavior. In particular, we establish quasi-Newton interpretations of Neumaier’s residual inverse iteration and Ruhe’s method of successive linear problems. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1007/s11075-017-0438-2 | Numerical Algorithms |
Keywords | Field | DocType |
Nonlinear eigenvalue problems, Inverse iteration, Iterative methods, Quasi-Newton methods | Convergence (routing),Mathematical optimization,Holomorphic function,Nonlinear system,Jacobian matrix and determinant,Iterative method,Mathematical analysis,Computational mathematics,Mathematics,Eigenvalues and eigenvectors,Inverse iteration | Journal |
Volume | Issue | ISSN |
79 | 1 | 1017-1398 |
Citations | PageRank | References |
2 | 0.38 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jarlebring Elias | 1 | 84 | 11.48 |
| Antti Koskela | 2 | 4 | 1.78 |
| Giampaolo Mele | 3 | 2 | 0.38 |