Determination of eigenvalues of real symmetric para-p diagonal matrices

Abstract

A method is presented for an accurate numerical determination of eigenvalues of real symmetric para-p diagonal matrices. The method takes advantage of the band structure to break up the matrix intop ×p blocks and performing algebraic operations including inversions on these blocks only, no matter what the size of the matrix is. The eigenvalues are determined independently one at a time. Thus any error in the determination of one eigenvalue does not affect the other eigenvalues. The method is ideally suited for the Schrödinger eigen alue problem of the anharmonic potentials, which is taken up in the following paper.