Best “ordering” for Floating-Point Addition

This correspondence examines the influence of the summation order on the numerical accuracy of the resulting sum when the addition is performed using floating-point, finite-precision arithmetic. A simple statistical model is used to find the relative performance of various addition procedures. It is shown that phrasing the question in terms of finding a best ordering is overly restrictive since the most natural and accurate procedures for performing the addition utilize the storage of intermediate sums as well as performing orderings.