Journal
MATHEMATICS
Volume 10, Issue 10, Pages -Publisher
MDPI
DOI: 10.3390/math10101676
Keywords
generalized eigenvalue problems; rank-structured matrix; SSS matrix; banded reduction
Categories
Funding
- NSFC [2021YFB0300101, 62073333, 61902411, 62032023, 12002382, 11275269, 42104078]
- 173 Program of China [2020-JCJQ-ZD-029]
- State Key Laboratory of High Performance Computing of China (HPCL) [202101-01]
- Guangdong Natural Science Foundation [2018B030312002]
- Program for Guangdong Introducing Innovative and Entrepreneurial Teams [2016ZT06D211]
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A novel algorithm is proposed in this paper to reduce a banded symmetric generalized eigenvalue problem to a banded symmetric standard eigenvalue problem, using the sequentially semiseparable (SSS) matrix techniques. The algorithm requires linear storage cost and offers potential for parallelism.
In this paper, a novel algorithm is proposed for reducing a banded symmetric generalized eigenvalue problem to a banded symmetric standard eigenvalue problem, based on the sequentially semiseparable (SSS) matrix techniques. It is the first time that the SSS matrix techniques are used in such eigenvalue problems. The newly proposed algorithm only requires linear storage cost and O(n(2)) computation cost for matrices with dimension n, and is also potentially good for parallelism. Some experiments have been performed by using Matlab, and the accuracy and stability of algorithm are verified.
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