A modified algorithm for computing the eigenvalues and the eigenvectors using the bimodal optical computer

Abstract

A modified algorithm is introduced for computing the eigenvalues and the eigenvectors of a positive definite matrix using the inverse iteration method and the bimodal optical computer (BOC). It is known that the inverse iteration method is sensitive to the choice of the initial value of the eigenvalue. This paper investigates the effects of the initial choice of the eigenvalue on the solution using the inverse iteration method and suggests a modification. The modified algorithm presented in this paper uses the Rayliegh quotient ratio to compute a good estimate of the initial guess of an eigenvalue. A skyscraper eigenvalue problem is used as an example in this paper to help illustrate the new algorithm.