Rayleigh quotient minimization method for symmetric eigenvalue problems

In this paper, we present a new method, which is referred to as the Rayleigh quotient minimization method, for computing one extreme eigenpair of symmetric matrices. This method converges globally and attains cubic convergence rate locally. In addition, inexact implementations and its numerical stability of the Rayleigh quotient minimization method are explored. Finally, we use numerical experiments to demonstrate the convergence properties and show the competitiveness of the new method for solving symmetric eigenvalue problems.