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