Efficient Reduction Algorithms for Banded Symmetric Generalized Eigenproblems via Sequentially Semiseparable (SSS) Matrices

Abstract

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(n2) 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.