Analysis and Improvement of Kahan's Summation Algorithm

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This paper shows an example in which Kahan's algorithm for summation is not at all effective and consider the reasons for the uneffectiveness. Next this paper proposes a new algorithm similar to Kahan's. Application of this new algorithm to the same and other examples show that the algorithm improves the results over Kahan's. Error analyses of the two algorithms show that in both algorithms the quantities approximating the accumulated errors can be obtained in the course of computations. In particular this quantities of the improved algorithm approximates the error more precisely than that of Kahan's. The cpu time of the improved algorithm is about 1.4 times that of Kahan's.

This paper shows an example in which Kahan's algorithm for summation is not at all effective, and consider the reasons for the uneffectiveness. Next, this paper proposes a new algorithm similar to Kahan's. Application of this new algorithm to the same and other examples show that the algorithm improves the results over Kahan's. Error analyses of the two algorithms show that, in both algorithms, the quantities approximating the accumulated errors can be obtained in the course of computations. In particular, this quantities of the improved algorithm approximates the error more precisely than that of Kahan's. The cpu time of the improved algorithm is about 1.4 times that of Kahan's.

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