A parallel algorithm for computing eigenvalues of very large real symmetric matrices on message passing architectures (Q1294603)

The symmetric Lanczos algorithm with no reorthogonalization is implemented on a message passing parallel machine. Two ways of distributing the matrix on the processors are compared, one pure row distribution scheme and one based on graph subdivision. It is found that the second scheme comes to advantage when there are more than about four processors. All processors compute eigenvalues of the resulting tridiagonal matrix, each of them for a specified part of the spectrum. The Cullum device is used to weed out spurious eigenvalue approximations.