Acceleration of convergence in solving the eigenvalue problem by matrix iteration using the power method

Abstract

A modification of the matrix iteration using the power method, in conjunction with Hotelling deflation, for the solution of the problem K.x = ω².M.x is here proposed. The problem can be written in the form D.x =λ.x, and the modification consists of raising the matrix D to an appropriate power p before carrying out the iteration process. The selection of a satisfactory value of p is investigated, based on the spacing between the eigenvalues. The effect of p on the accuracy of the results is also discussed.