An Estimate for the Condition Number of a Matrix
Alan Cline, C Moler, G. W. Stewart, James Hardy Wilkinson · SIAM Journal on Numerical Analysis · 1979
It is important in practice when solving linear systems to have an economical method for estimating the condition number $\kappa (A)$ of the matrix of coefficients. An algorithm involving $O(n^2 )$ arithmetic operations is described; it gives a reliable indication of the order of magnitude of $\kappa (A)$.