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Accession Number:
AD0269604
Title:
REMARKS ON THE CONTINUED FRACTION CALCULATION OF EIGENVALUES AND EIGENVECTORS
Corporate Author:
HARVARD UNIV CAMBRIDGE MASS MALLINCKRODT LAB
Report Date:
1960-12-01
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
Pages:
0001
Contract Number:
N5ORI186614
File Size:
0.00MB
