Abstract

A method for locating the mlntmum eigenvalue and its corresponding eigenvector is considered. The convergence rate of the Rayleigh quotient iteration (RQI) is cubic. However, unfortunately, the RQI may not always locate the minimum eigenvalue. In this paper, a modified Rayleigh quotient iteration (MRQI) that can always locate the minimum eigenpair is proposed and Mathematical properties of the MRQI are investigated. Based on the MRQI, a fast algorithm to locate minimum eigenpair will be proposed. It can locate multiple minimum eigenvalues, while others which employ an inclusion interval cannot.

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