# Accession Number:

## AD0269604

# Title:

## REMARKS ON THE CONTINUED FRACTION CALCULATION OF EIGENVALUES AND EIGENVECTORS

# Descriptive Note:

# Corporate Author:

## HARVARD UNIV CAMBRIDGE MASS MALLINCKRODT LAB

# Personal Author(s):

# Report Date:

## 1960-12-01

# Pagination or Media Count:

## 1.0

# Abstract:

For eigenvalue problems in which the secular determinant has tridiagonal form, e.g., the rigid asymmetric rotor the secular equation may be written in the form fl equals 0, where fl is a continued fraction and l an eigenvalue. Furthermore, if the secular problem is of nth order, then the continued fraction l may be developed in n different ways. Since the eigenvalues are roots of a function fl, it is convenient to find the eigenvalues by means of the Newton-Raphson iterative procedure. This requires that the derivative of fl with respect to lfl be determined. An exact expression for fl is derived and it is shown that fl is in fact the norm of the eigenvector belonging to the eigenvalue l. A simple recursion formula, in continued fraction form, for the eigenvector elements is also derived. Author