A Stable Divide and Conquer Algorithm for the Unitary Eigenproblem
Ming Gu, Robert Guzzo, Xuebin Chi, Xing-Qin Cao · SIAM Journal on Matrix Analysis and Applications · 2003
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 modification 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.