A PARALLELIZABLE EIGENSOLVER FOR REAL DIAGONALIZABLE MATRICES WITH REAL EIGENVALUES

In this paper, preliminary research results on a new algorithm for fin ding all the eigenvalues and eigenvectors of a real diagonalizable mat rix with real eigenvalues are presented. The basic mathematical theory behind this approach is reviewed and is followed by a discussion of t he numerical considerations of the actual implementation. The numerica l algorithm has been tested on thousands of matrices on both a Gray-2 and an IBM RS/6000 Model 580 workstation. The results of these tests a re presented. Finally, issues concerning the parallel implementation o f the algorithm are discussed. The algorithm's heavy reliance on matri x-matrix multiplication, coupled with the divide and conquer nature of this algorithm, should yield a highly parallelizable algorithm.