A Set of Counter-Examples to Three Condition Number Estimators
Alan Cline, R.K. Rew · SIAM Journal on Scientific and Statistical Computing · 1983
The estimation of the condition number of a matrix relative to inversion is important for bounding the errors in computer solutions of linear systems of equations. Three methods of estimation are shown to underestimate the true condition number of particular matrices by arbitrarily large factors. One of the methods is that employed in the LINPACK software package.