  Gaussian elimination (GE) is the most used dense linear solver. Error
analysis of GE with selected pivoting strategies on well-conditioned systems
can focus on studying the behavior of growth factors. Although exponential
growth is possible with GE with partial pivoting (GEPP), growth tends to stay
much smaller in practice. Support for this behavior was provided recently by
Huang and Tikhomirov's average-case analysis of GEPP, which showed GEPP growth
factors for Gaussian matrices stay at most polynomial with very high
probability. GE with complete pivoting (GECP) has also seen a lot of recent
interest, with improvements to both lower and upper bounds on worst-case GECP
growth provided by Bisain, Edelman and Urschel in 2023. We are interested in
studying how GEPP and GECP behave on the same linear systems as well as
studying large growth on particular subclasses of matrices, including
orthogonal matrices. Moreover, as a means to better address the question of why
large growth is rarely encountered, we further study matrices with a large
difference in growth between using GEPP and GECP, and we explore how the
smaller growth strategy dominates behavior in a small neighborhood of the
initial matrix.
