Growth factor and expected growth factor of some pivoting strategies

Several definitions of growth factors for Gaussian elimination are compared. Some new pivoting strategies, intermediate between partial pivoting and rook pivoting, are introduced. For random matrices, an approximation of the average normalized growth factor associated with several pivoting strategies is computed and analyzed. A stationary behavior of the expected growth factors of the new pivoting strategies is observed. Bounds for the growth factors of these pivoting strategies are provided. It is also shown that partial pivoting by columns produces small growth factors for matrices appearing in practical observations and for which the growth factors produced by partial pivoting are very large.