A Generalized Kahan-Babuska-Summation-Algorithm

Abstract

In this article, we combine recursive summation techniques with Kahan-Babuska type balancing strategies [1], [7] to get highly accurate summation formulas. An i-th algorithm have only error beyond 1upl and thus allows to sum many millions of numbers with high accuracy. The additional afford is a small multiple of the naive summation. In addition we show that these algorithms could be modified to provide tight upper and lower bounds for use with interval arithmetic. [PUBLICATION ABSTRACT]