Name
Abstract | ||
|---|---|---|
We first provide existence and uniqueness conditions for the solvability of an algebraic eigenvalue problem with eigenvector nonlinearity. We then present a local and global convergence analysis for a self-consistent field (SCF) iteration for solving the problem. The well-known sin theorem in the perturbation theory of Hermitian matrices plays a central role. The near-optimality of the local convergence rate of the SCF iteration revealed in this paper is demonstrated by examples from the discrete Kohn-Sham eigenvalue problem in electronic structure calculations and the maximization of the trace ratio in the linear discriminant analysis for dimension reduction. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1137/17M115935X | SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS |
Keywords | Field | DocType |
nonlinear eigenvalue problem,self-consistent field iteration,convergence analysis | Convergence (routing),Applied mathematics,Uniqueness,Nonlinear system,Algebraic number,Mathematical analysis,Eigenvalues and eigenvectors,Mathematics | Journal |
Volume | Issue | ISSN |
39 | 3 | 0895-4798 |
Citations | PageRank | References |
5 | 0.40 | 0 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yun-Feng Cai | 1 | 21 | 4.06 |
| Lei-Hong Zhang | 2 | 87 | 12.00 |
| Zhaojun Bai | 3 | 661 | 107.69 |
| Ren-Cang Li | 4 | 278 | 50.05 |