Title of Paper:Simultaneous band reduction of two symmetric matrices

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Date of Publication:2019-01-01

Journal:Computers and Mathematics with Applications

Volume:77

Issue:8

Page Number:2207-2220

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

Abstract: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