A parallel processed scheme for the eigenproblem of positive definite matrices

This paper deals with the eigenproblem of positive definite matrices. A numerical algorithm, to find the largest eigenvalues of a full positive definite matrix using Householder reflections, is described. The proposed algorithm can be used to find all the eigenvalues of a symmetric matrix or at least the first few largest ones. The scheme is proved to be convergent and the convergence rate is calculated. The full matrix is operated upon, at each iteration; hence one could use the APL programming language to write down a very brief code to implement the program.