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The growth factor in Gaussian elimination measures how large the entries ofan LU factorization can be relative to the entries of the original matrix. Itis a key parameter in error estimates, and one of the most fundamental topicsin 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 -- thefirst improvement upon Wilkinson's original 1961 bound of $2 \, n ^{0.25\ln n+0.5}$.

A New Upper Bound For the Growth Factor in Gaussian Elimination with Complete Pivoting