Parallel algorithm for the reduction to tridiagonal form for eigendecomposition

One-sided orthogonal transformations which orthogonalize columns of a matrix are related to methods for finding singular values. They have the advantages of lending themselves to parallel and vector implementations and simplifying access to the data by not requiring access to both rows and columns. They can be used to find eigenvalues when the matrix is given in factored form. Here, a finite sequence of transformations leading to a partial orthogonalization of the columns is described. This permits a tridiagonal matrix whose eigenvalues are the squared singular values to be derived. The implementation on the Fujitsu VPP series is discussed and some timing results are presented.