Accurate Floating-Point Product and Exponentiation
Accurate Floating-Point Product and Exponentiation
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DOI：
10.1109/tc.2008.215
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发表时间：
2009-07
影响因子：
3.7
通讯作者：
S. Graillat
中科院分区：
文献类型：
--
作者：
S. Graillat
几种不同的技术和软件旨在提高在固定的有限精度计算的结果的准确性。在这里，我们专注于提高浮点数乘积精度的方法。我们表明，计算结果是准确的，如果计算在两倍的工作精度。该算法很简单，因为它只需要在与给定数据相同的工作精度下进行浮点数的加法、减法和乘法。这样的算法可以是有用的，例如计算三角矩阵的行列式和评估多项式时，表示为根积形式。它也可以用来计算浮点数的整数幂。
Several different techniques and softwares intend to improve the accuracy of results computed in a fixed finite precision. Here, we focus on a method to improve the accuracy of the product of floating-point numbers. We show that the computed result is as accurate as if computed in twice the working precision. The algorithm is simple since it only requires addition, subtraction, and multiplication of floating-point numbers in the same working precision as the given data. Such an algorithm can be useful for example to compute the determinant of a triangular matrix and to evaluate a polynomial when represented by the root product form. It can also be used to compute the integer power of a floating-point number.