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

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, Pnm(cos ϑ). 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 Pnm (cos ϑ) to Pnn(cos ϑ)] is by far the superior computational scheme.