This paper considers a probabilistic model for floating-point computation in which the roundoff errors are represented by bounded random variables with mean zero. Using this model, a probabilistic bound is derived for the forward error of the computed sum of n real numbers. This work improves upon existing probabilistic bounds by holding to all orders, and as a result provides informative bounds for larger problem sizes.

翻译：本文考虑了浮动点计算的一个概率模型,在这种模型中,四舍五入的误差由约束随机变量代表,平均为零。 使用这个模型,对实际数字的计算总和的远端误差,可以得出概率误差。 这项工作通过持有所有订单,改进了现有的概率误差,从而为更大的问题大小提供了信息误差。