Abstract

Moler and Morrison have described an iterative algorithm for the computation of the Pythagorean sum (a ' + b2)" ' of two real numbers a and b. This algorithm is immune to unwarrantedfloating-point overjows, has a cubic rate of convergence, and is easily transportable. This paper, which shows that the algorithm is essentially Harley's method applied to the computation of square roots. provides a generalization to any order of convergence. Formulas of orders 2 through 9 are illustrated with numerical examples. The generalization keeps the number of floating-point divisions constant and should be particularly useful for computation in high-precision floating-point arithmetic. 1.

Citations

47	Iterative methods for the solutions of equations - Traub - 1982
3	Replacing Square Roots by Pythagorean Sums - Moler, Morrison - 1983