@article{Cline1979ANEF,
title={AN ESTIMATE FOR THE CONDITION NUMBER OF A MATRIX},
author={A. K. Cline and C. Moler and G. Stewart and J. H. Wilkinson},
journal={SIAM Journal on Numerical Analysis},
year={1979},
volume={16},
pages={368-375}
}

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 $\kappa (A)$.