The growth factor in Gaussian elimination measures how large the entries of an LU factorization can be relative to the entries of the original matrix. It is a key parameter in error estimates, and one of the most fundamental topics in numerical analysis. We produce an upper bound of $n^{0.2079 \ln n +0.91}$ for the growth factor in Gaussian elimination with complete pivoting -- the first improvement upon Wilkinson's original 1961 bound of $2 \, n ^{0.25\ln n +0.5}$.

翻译：高斯消元法中的增长因子用于衡量LU分解中元素相对于原始矩阵元素的可能放大程度。该参数是误差估计中的关键指标，也是数值分析中最基础的课题之一。本文针对完全主元选取的高斯消元法，提出了增长因子的新上界$n^{0.2079 \ln n +0.91}$——这是对Wilkinson于1961年提出的原始上界$2 \, n ^{0.25\ln n +0.5}$的首次改进。