Experiments and analysis for the condition numbers of random triangular matrices
Lin Li-dong · Journal of Jinan University · 2001
D.Viswanath and L.N.Trefethen discussed the condition numbers of random triangular matrices in 1998.Two points were showed: the 2-norm condition numbers k n of random triangular matrices satisfy nk n-2 almost surely as n-∞,and the 2-norm condition numbers k n of random unit triangular matrices satisfy nk n-1.305 683 410... almost surely as n-∞.In this paper we point out that the conclusion seem not in according with the numerical experiments . The numerical experiments also indicate that the condition numbers of random matrices tend to be stable, and Gaussian elimination is almost stable. The strictly proof will be further researched.