An Algorithm for Simultaneous Band Reduction of Two Dense Symmetric Matrices (Fusion of theory and practice in applied mathematics and computational science)

Abstract

In this paper, we propose an algorithm for simultaneously reducing two dense symmetric matrices to band form with the same bandwidth by congruent transformations. The simultaneous band reduction can be considered as an extension of the simultaneous tridiagonalization of two dense symmetric matrices. In contrast to algorithms of simultaneous tridiagonalization that are based on Leve1-2 BLAS (Basic Linear Algebra Subroutine) operations, our band reduction algorithm is devised to take full advantage of Leve1-3 BLAS operations for better performance. Numerical results are presented to illustrate the effectiveness of our algorithm.