Pivot size in gaussian elimination

LetA = (a _ij ) be a real n x n matrix such that |a _ij | < 1. It has been conjectured by WILKINSON that if the process of Gaussian elimination with complete pivoting is applied to A then all the pivots are less than or equal to n in absolute value. This conjecture is proved forn=4.Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.