Quick Search:    advanced search

GSW Home   GeoRef Home   My GSW Alerts   Contact GSW   About GSW   Journals List   Help

This Article Full Text (PDF) References Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by WIGGINS, R. A. Articles by SAITO, M. Search for Related Content GeoRef GeoRef Citation

Evaluation of computational algorithms for the Associated Legendre Polynomials by interval analysis

RALPH A. WIGGINS^* and MASANORI SAITO

DEPARTMENT OF EARTH AND PLANETARY SCIENCES MASSACHUSETTS INSTITUTE OF TECHNOLOGY, CAMBRIDGE, MASSACHUSETTS 02139

Abstract

An interval arithmetic that consists of tracing the number of significant figures during each calculation is applied to computational algorithms for the Associated Legendre Polynomial, P_n^m(cos ). The results indicate that the interval arithmetic scheme is a good estimator for the propagation of round-off errors and that one particular algorithm [a recurrence relation that relates P_n^m (cos ) to P_nⁿ(cos )] is by far the superior computational scheme.

Footnotes

^* Now at the Department of Physics, University of Toronto, Toronto, Ontario, Canada.

Now at the Geophysical Institute, Faculty of Science, University of Tokyo, Tokyo, Japan.