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Rayleigh Quotient Iterative Alsorithms for

Frequency Estimation and Direction Finding

**Jyh-Chern Ho and Jar-Ferr Yang**

National Cheng Kung University,

Tainan, Taiwan 70101, Republic of China

The Rayleigh quotient iterative algorithm with computational complexity O(N ) was originally suggested for finding the eigenvalues of an N-by-N matrix with fast convergence rate. In this paper, a modified payleigh quotient iterative (MRQI) algorithm is proposed to track the desired roots, i.e. the roots close to the unit circle of spectral polynomials. The MRQI algorithm associated with a zero suppression technique, called the parallel Rayleigh Quotient iterative (PRQI) algotithm, is further proposed to assure that rooting processors converge to different desired principal roots of spectral polynomials. The PROI alglrithm only with computational complexity O(N) tracks the nonstationary roots of spectral polynomials even starting from random initializations. Simulations show the better tracking performance of the suggested algorithm compared to that of the gradient Newton algorithm[11].

Keywords: parallel computation, nonstationary roots, computation complexity, deflation, principal toots, random initializations

Received December 1, 1991; revised April 7, 1992.

Communicated by Fhing-Fa Wang.
**FERENCE**

- Yang, J. F. and Kaveh, M., "Adaptive Algorithms for Tracking Roots of Nonstationary Polynomials,"
*Proc. IEEE Int. Conf. Accoust., Speech, Signal processing*, 1989, pp. 1162-1165.