A Jacobi-Like Algorithm for Computing the Schur Decomposition of a Nonhermitian Matrix

Abstract

This paper describes an iterative method for reducing a general matrix to upper triangular form by unitary similarity transformations. The method is similar to Jacobi’s method for the symmetric eigenvalue problem in that it uses plane rotations to annihilate off-diagonal elements, and when the matrix is Hermitian it reduces to a variant of Jacobi’s method. Although the method cannot compete with the QR algorithm in serial implementation, it admits of a parallel implementation in which a double sweep of the matrix can be done in time proportional to the order of the matrix.