A direct method for completing eigenproblem solutions on a parallel computer

AbstractThe computation of eigenvalues and eigenvectors of a real symmetric matrix A with distinct eigenvalues can be speeded up at the end of the Jacobi process when the off-diagonal elements have become sufficiently small for A to be regarded as a perturbation of a diagonal matrix. A leading-order approximation to the eigensolution is calculated by formulae particularly suitable for the distributed array processor (DAP). A single application of this direct method reduces A to diagonal form and is asymptotically equivalent to an entire sweep of the Jacobi method