John Urschel proves that an n×n Gaussian matrix’s growth factor under partial pivoting is rarely much larger than √n—resolving a longstanding conjecture by Nick Trefethen. The paper also sharpens results for other random matrices. 📊🧮 #NumericalAnalysis #Math https://arxiv.org/abs/2610.06785
arXiv.orgOn the Growth Factor of Random MatricesGaussian elimination is the oldest and most popular method for solving a linear system. Its numerical stability for a given matrix is controlled by the growth factor, a measure of how large entries can become during elimination. In this work, we prove a number of new results regarding the growth factor of random matrices. First, we provide tight estimates for the growth factor of a matrix precondi