An improved Laguerre eigensolver for unsymmetric matrices

A Laguerre iteration procedure is described for finding the eigenvalues of unsymmetric matrices with improved efficiency. Compared to the QR method, t he processing time for dense matrices is reduced by roughly a factor of 1.6 and for sparse matrices by a factor of up to 2.8 without sacrificing accur acy. This is achieved primarily by means of new procedure for reducing the original matrix to sparse Hessenberg form. Alternatively, the Laguerre proc edure will typically provide one additional significant digit, compared to the QR method, when allowed to run for as long as the QR method.