Computing the sign of a dot product sum

Authors:
Yong-Kang Zhu;Jun-Hai Yong;Guo-Qin Zheng
Affiliations:
School of Software, Tsinghua University, Beijing, P. R. China;School of Software, Tsinghua University, Beijing, P. R. China;School of Software, Tsinghua University, Beijing, P. R. China
Venue:
CIS'04 Proceedings of the First international conference on Computational and Information Science
Year:
2004

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Abstract

A real number usually cannot be exactly represented by a floating-point number in a computer. Namely, a floating-point number frequently stands for any real number in a specific interval. In this paper, we present a method for computing the sign of a dot product sum. Each initial datum that is a floating-point number is considered as an interval. With interval analysis and floating-point summation methods, an explicit formula for calculating the minimal interval of a dot product sum is presented. Error analysis and some examples are provided as well.