A stable divide and conquer algorithm for the unitary eigenproblem

We present a divide and conquer algorithm for computing the eigendecomposition of a unitary upper Hessenberg matrix H. Previous divide and conquer approaches suffer a potential loss of orthogonality among the computed eigenvectors of H. Using a backward stable method based on previous work by Gu and Eisenstat in the rank-one modi. cation of the symmetric eigenproblem, our algorithm provides a backward stable method for computing the eigenvectors. The method also compares well against the efficiency of other available methods.