A distillation algorithm for floating-point summation

被引:16
作者
Anderson, IJ [1 ]
机构
[1] Univ Huddersfield, Sch Comp & Math, Huddersfield HD1 3DH, W Yorkshire, England
关键词
floating-point summation; rounding error; distillation;
D O I
10.1137/S1064827596314200
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The addition of two or more floating-point numbers is fundamental to numerical computations. This paper describes an efficient "distillation" style algorithm which produces a precise sum by exploiting the natural accuracy of compensated cancellation. The algorithm is applicable to all sets of data but is particularly appropriate for ill-conditioned data, where standard methods fail due to the accumulation of rounding error and its subsequent exposure by cancellation. The method uses only standard floating-point arithmetic and does not rely on the radix used by the arithmetic model, the architecture of specific machines, or the use of accumulators.
引用
收藏
页码:1797 / 1806
页数:10
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