Expected growth factors of pivoting strategies for Gauss elimination
V. Cortés, Juan Manuel Peña · 2003
Several definitions of growth factors for Gaussian elimination are compared, including an approximation of the average normalized growth factor for random matrices introduced in [3]. Some new pivoting strategies, intermediate between partial pivoting and rook pivoting, are introduced. For instance, double partial pivoting and triple partial pivoting. A stationary behavior of the expected growth factors of these new pivoting strategies is observed and bounds for the growth factors are provided in [1]. Stability of Gauss Jordan elimination for these pivoting strategies is considered. A theoretical bound for the growth factor of scaled partial pivoting strategies was derived in [2]. The expected growth factor of scaled partial pivoting strategies is analyzed and compared with the expected growth factors corresponding to other pivoting strategies. 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.