MOORE, JB and MAHONY, RE and HELMKE, U (1994) NUMERICAL GRADIENT ALGORITHMS FOR EIGENVALUE AND SINGULAR-VALUE CALCULATIONS. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 15 (3). pp. 881-902. ISSN 0895-4798,
Full text not available from this repository.Abstract
Recent work has shown that the algebraic question of determining the eigenvalues, or singular values, of a matrix can be answered by solving certain continuous-time gradient flows on matrix manifolds. To obtain computational methods based on this theory, it is reasonable to develop algorithms that iteratively approximate the continuous-time flows. In this paper the authors propose two algorithms, based on a double Lie-bracket equation recently studied by Brockett, that appear to be suitable for implementation in parallel processing environments. The algorithms presented achieve, respectively, the eigenvalue decomposition of a symmetric matrix and the singular value decomposition of an arbitrary matrix. The algorithms have the same equilibria as the continuous-time flows on which they are based and inherit the exponential convergence of the continuous-time solutions.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | VALUE DECOMPOSITION; TODA LATTICE; QR ALGORITHM; EQUATIONS; FLOW; EIGENVALUE DECOMPOSITION; SINGULAR VALUE DECOMPOSITION; NUMERICAL GRADIENT ALGORITHM |
| Depositing User: | Dr. Gernot Deinzer |
| Last Modified: | 19 Oct 2022 08:40 |
| URI: | https://pred.uni-regensburg.de/id/eprint/53224 |
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