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A sorted partial jacobi method and its convergence analysis

✍ Scribed by Hongyuan Zha; Zhenyue Zhang

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
961 KB
Volume
270
Category
Article
ISSN
0024-3795

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✦ Synopsis

Jacobi methods for computing the eigendecomposition of a class of so-called low-rank-plus-shift symmetric matrices are investigated. An order-of-magnitude reduction in the computational complexity can be achieved for this special class of matrices by terminating the Jacobi sweep early in a cyclic ordering. It is proved that these partial sweeps combined with sorting the diagonals still deliver quadratic convergence. It is also shown that useful results can still be obtained even if the low-rank-plus-shift structure only holds approximately.

πŸ“œ SIMILAR VOLUMES

A refined jacobi-davidson method and its
A refined jacobi-davidson method and its correction equation
✍ Shaoqiang Feng; Zhongxiao Jia πŸ“‚ Article πŸ“… 2005 πŸ› Elsevier Science 🌐 English βš– 602 KB

A central problem in the Jacobi-Davidson method is to expand a projection subspace by solving a certain correction equation. It has been commonly accepted that the correction equation always has a solution. However, it is proved in this paper that this is not true. Conditions are given to decide whe