Parallel Computation of the Eigenstructure of Toeplitz-plus-Hankel Matrices on Multicomputers

In this paper we present four parallel algorithms to compute any group of eigenvalues and eigenvectors of a Toeplitz-plus-Hankel matrix. These algorithms parallelize a method that combines the bisection technique with a fast root-finding procedure to obtain each eigenvalue. We design a parallel algorithm that applies a static distribution of the calculations among processors and three algorithms that use the farming technique to dynamically balance the load. All the algorithms have been implemented on a Multicomputer based on a network of transputers. We also present a study of the experimental performances and compare the different algorithms. The results obtained are in many cases very near to the maximum theoretical performances we can expect.