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. © Springer-Verlag 2004.
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Zhu, Y. K., Yong, J. H., & Zheng, G. Q. (2004). Computing the sign of a dot product sum. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 3314, 1086–1092. https://doi.org/10.1007/978-3-540-30497-5_167