REMARKS ON THE CONTINUED FRACTION CALCULATION OF EIGENVALUES AND EIGENVECTORS
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 f(l') equals 0, where f(l') 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 f(l'), it is convenient to find the eigenvalues by means of the Newton-Raphson iterative procedure. This requires that the derivative of f(l') with respect to l(f'(l) be determined. An exact expression for f'(l) is derived and it is shown that f'(l') 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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1960
- Accession Number
- AD0269604
Entities
People
- Jerome D. Swalen
- Louis Pierce
Organizations
- Harvard University