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论文类型： 期刊论文

发表时间： 2019-01-01

发表刊物： Computers and Mathematics with Applications

卷号： 77

期号： 8

页面范围： 2207-2220

关键字： Computer architecture; Matrix algebra, Band reduction; Matrix operations; Matrix pencil; Numerical results; Symmetric matrices; Tridiagonalization; Vector operations; WY representation, Linear transformations

摘要： In this paper, we consider simultaneous band reduction of two dense symmetric matrices by congruent transformations. The ideas of simultaneous tridiagonalization are generalized to propose an efficient algorithm for the simultaneous band reduction. In contrast to the algorithms of simultaneous tridiagonalization which are mainly based on matrix–vector operations, the proposed algorithm of simultaneous band reduction has the advantage that matrix–matrix operations can be fully used to achieve better performance on modern computer architecture. Numerical results are presented to illustrate the effectiveness of our proposed algorithm. © 2018 Elsevier Ltd