Abstract
This paper concerns a class of monotone eigenvalue problems with eigenvector nonlinearities (mNEPv). The mNEPv is encountered in applications such as the computation of joint numerical radius of matrices, best rank-one approximation of third-order partial-symmetric tensors, and distance to singularity for dissipative Hamiltonian differential-algebraic equations. We first present a variational characterization of the mNEPv. Based on the variational characterization, we provide a geometric interpretation of the self-consistent field (SCF) iterations for solving the mNEPv, prove the global convergence of the SCF, and devise an accelerated SCF. Numerical examples demonstrate theoretical properties and computational efficiency of the SCF and its acceleration.
| Original language | English |
|---|---|
| Pages (from-to) | 84-111 |
| Number of pages | 28 |
| Journal | SIAM Journal on Matrix Analysis and Applications |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2024 |
Bibliographical note
Publisher Copyright:© by SIAM. Unauthorized reproduction of this article is prohibited.
Funding
ast Received by the editors September 28, 2022; accepted for publication (in revised form) by K. Meerbergen August 22, 2023; published electronically January 11, 2024. https://doi.org/10.1137/22M1525326 Funding: The work of the first author was supported by NSF DMS-1913364. The work of the second author was supported by NSF DMS-2110731. dagger Department of Computer Science, University of California at Davis, Davis, CA 95616 USA ([email protected]). ddagger Department of Mathematics, University of Kentucky, Lexington, KY 40506 USA (Ding.Lu@ uky.edu).
| Funders | Funder number |
|---|---|
| National Science Foundation Arctic Social Science Program | DMS-2110731, DMS-1913364 |
Keywords
- convergence analysis
- geometry of SCF
- nonlinear eigenvalue problem
- self-consistent field iteration
- variational characterization
ASJC Scopus subject areas
- Analysis