Highly concurrent Toeplitz eigen-system solver for high resolution spectral estimation

In this paper, we develop a highly concurrent Toeplitz Eigen-System Solver (TES) for computing the minimum eigenvalue and associated eigenvector of a N by N symmetric Toeplitz matrix. Conventionally, solving an eigen-system will require O(N³) times with sequential machine; or O(N²) time with O(N) processing units. By exploring the Toeplitz structure and adopting a Rayleigh quotient iteration, the TES can solve for the desired minimum eigenvalue in O(KN) time with N processors and K iterations. The development of TES offers a fast algorithm to implement the Pisarenko´s high resolution spectral estimation technique.