The conventional rounding error analysis provides worst-case bounds with an associated failure probability and ignores the statistical property of the rounding errors. In this paper, we develop a new statistical rounding error analysis for random matrix computations. Such computations have numerous applications in the field of wireless communications, signal processing, and machine learning. By assuming the relative errors are independent random variables, we derive the approximate closed-form expressions for the expectation and variance of the rounding errors in various key computations for random matrices. Numerical experiments validate the accuracy of our derivations and demonstrate that our analytical expressions are generally at least two orders of magnitude tighter than alternative worst-case bounds, exemplified through the inner products.

翻译：传统的舍入误差分析提供了带有相关失效概率的最坏情况界，但忽略了舍入误差的统计特性。本文针对随机矩阵计算提出了一种新的统计舍入误差分析方法。此类计算在无线通信、信号处理和机器学习领域有广泛应用。通过假设相对误差为独立随机变量，我们推导了随机矩阵在多种关键计算中舍入误差的期望与方差的近似闭式表达式。数值实验验证了推导结果的准确性，并表明我们的解析表达式通常比替代的最坏情况界至少紧致两个数量级，以内积计算为例进行了说明。