On Incremental Condition Estimators in the 2-Norm

The paper deals with estimating the condition number of triangular matrices in the Euclidean norm. The two main incremental methods, based on the work of Bischof and on the later work of Duff and Vömel, are compared. The paper presents new theoretical results revealing their similarities and differences. As typical in condition number estimation, there is no universal always-winning strategy, but theoretical and experimental arguments show that the clearly preferable approach is the algorithm of Duff and Vömel when appropriately applied to both the triangular matrix itself and its inverse. This leads to a highly accurate incremental condition number estimator.