Parallel Rayleigh quotient iterative algorithm for rooting nonstationary spectral polynomials

A parallel Rayleigh quotient iterative algorithm (PRQI) associated with the zeros extraction technique which assures that each processor converges to a different desired root is proposed. The suggested algorithm with arbitrary initialization can automatically converge to the desired roots which are close to the unit circle. The proposed algorithm has a computation complexity of O(N) for rooting spectrum polynomials. Simulations show that the suggested algorithm has a better tracking performance than the Gauss-Newton method and the gradient Newton algorithm