论文标题
有效的总和算法，用于平行数值方法的准确性，收敛性和可重复性
An Efficient Summation Algorithm for the Accuracy, Convergence and Reproducibility of Parallel Numerical Methods
论文作者
论文摘要
如今，在工程和科学中，平行计算在几个应用程序领域中都是无处不在的。这些计算依赖于IEEE754标准指定的浮点算术。在这种情况下，到处使用的计算的基本砖是数字序列的总和。此和在浮点算术中遇到许多数值错误。为了减轻此问题，我们引入了一种新的并行算法，用于求和一系列浮点数。该算法可以通过处理器数量轻松扩展，首先添加相同指数的数字。在本文中，我们的主要贡献是对其相对于几种属性的效率进行广泛的分析：准确性，收敛性和可重复性。为了显示我们的算法的有用性，我们选择了一组代表性的数值方法，即Simpson，Jacobi，Lu分解和迭代的功率方法。
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of computation, used everywhere, is the sum of a sequence of numbers. This sum is subject to many numerical errors in floating-point arithmetic. To alleviate this issue, we have introduced a new parallel algorithm for summing a sequence of floating-point numbers. This algorithm which scales up easily with the number of processors, adds numbers of the same exponents first. In this article, our main contribution is an extensive analysis of its efficiency with respect to several properties: accuracy, convergence and reproducibility. In order to show the usefulness of our algorithm, we have chosen a set of representative numerical methods which are Simpson, Jacobi, LU factorization and the Iterated power method.
