A Divide and Conquer Method for the Unitary Eigenproblem and Applications

In divide and conquer methods for eigenproblems, the original eigenproblem is split into several smaller subproblems by using rank one modifications. Many of the subproblems can be solved in parallel, and from their solutions the solution of the original eigenproblem can be determined. This approach has for symmetric matrices been developed by Cuppen and refined by Dongarra and Sorensen. We describe a divide and conquer method for the computation of eigenvalues and eigenvectors of unitary matrices. The unitary matrices are represented in Schur parametric form. We also discuss the application of the unitary eigenproblem to the computation of Pisarenko frequency estimates in signal processing.