Research On The Two Acceleration Techniques Of Rayleigh Quotient For Subspace Iteration Method

In this paper,we consider the subspace iteration method for solving large symmetriceigenproblems,In order to accelerate the convergence rate, we improve the originalmethod with acceleration technique, and present two new algorithms In my the first proposed algorithm,A combination of the latest matrix received byinverse iteration and the Ritz matrix is formed involving an undetermined parametermatrix ,which is determined by minimizing the Rayleigh quotient,then it will near theminimal eigenvector. In my the second proposed algorithm,We create a combination as the same as thefirst one ,but in the second one the combination involving an undetermined parametermatrix ,which is determined by minimizing the Rayleigh quotient is formed by thelatest matrix received by a shifted inverse iteration and the Ritz matrix,thenaccelerate the convergence rate of subspace. In the paper ,We analysis the choosing method of the parameter matrix and its someproperty, the numerical stability and convergence . Our numerical results show that thetwo proposed algorithms are superior to the original subspace iteration method.