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：高斯消去法中的增长因子衡量了LU分解中元素相对于原始矩阵元素的最大可能增长幅度。它是误差估计中的关键参数，也是数值分析中最基础的主题之一。针对完全主元高斯消去法的增长因子，我们得到了一个上界$n^{0.2079 \ln n +0.91}$——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。