Estimating Matrix Condition Numbers
Dianne Prost O’Leary · SIAM Journal on Scientific and Statistical Computing · 1980
In this note we study certain estimators for the condition number of a matrix which, given an $LU$ factorization of a matrix, are easily calculated. The main observations are that the choice of estimator is very norm-dependent, and that although some simple estimators are consistently bad, none is consistently best. These theoretical conclusions are confirmed by experimental data, and recommendations are made for the one and infinity norms.