How to Compute the Area of a Triangle: a Formal Revisit with a tighter error bound
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چکیده
Mathematical values are usually computed using well-known mathematical formulas without thinking about their accuracy, which may turn awful with particular instances. This is the case for the computation of the area of a triangle. When the triangle is needle-like, the common formula has a very poor accuracy. Kahan proposed in 1986 an algorithm he claimed correct within a few ulps. Goldberg took over this algorithm in 1991 and gave a precise error bound. This article presents a formal proof of this algorithm, investigations in case of underflow and a new improvement of its error bound.
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تاریخ انتشار 2013