An interactive method for the eigenvalue problem for matrices

Abstract

The algorithm described in this article uses Householder reflections to obtain the largest eigenvalue of a full positive definite matrix. The algorithm can be used to obtain all the eigenvalues of a symmetric matrix and may be suitable for a parallel processing machine. We also consider the differential equations analogue of this method and prove the convergence of that method together with the convergence rates. Finally some numerical examples are given. This algorithm is very suitable to determine the eigenvalues in an interactive environment. Unlike the QL algorithm the full matrix is operated upon at each stage of the iterative process, hence one could use the APL programming language to write a very brief code to implement this program. © 1990.