Parallel Homotopy Algorithm for the Symmetric Tridiagonal Eigenvalue Problem

The parallel homotopy algorithm for finding few or all eigenvalues of a symmetric tridiagonal matrix is presented. The computations were executed on an NCUBE, a distributed memory multiprocessor. The numerical results show that the performance of our algorithm is strongly competitive with “divide and conquer” and bisection/multisection algorithms. The almost 100 percent efficiency seems to suggest that the natural parallelism of the homotopy method makes the algorithm an excellent candidate for a variety of architectures.