A parallel QR algorithm for the symmetrical tridiagonal eigenvalue problem

A parallel/pipelined algorithm and its architecture are proposed to solve the symmetric eigenvalue problem. This algorithm is based on Given's rotations, and it is associated with the initial reduction of the dense matrix to a tridiagonal one using Householder's transformations. The performance of this algorithm is described and compared to the performance of the sequential one. It can be shown that the cost of the eigendecomposition falls from O(m*n) to O(m+n), where m and n denote the matrix order and the number of iterations, respectively. This algorithm is mapped on m processors to compute the eigenvalues and eigenvectors simultaneously.< >