Some Condition-Number bounds for the Gaussian Elimination Process

It is well-known that Gaussian Elimination is equivalent to LU decomposition. This paper shows that if Gaussian Elimination is applied to a well-conditioned matrix, and if an increase in element size is observed during the elimination process, then both the triangular factors will be badly conditioned. It is further shown that the effect of partial pivoting is to place an upper bound upon the condition number of the lower triangular factor.