On Incremental Condition Estimators in the 2-norm

0422614 - ÚI 2015 RIV US eng J - Journal Article
Duintjer Tebbens, Jurjen - Tůma, Miroslav
On Incremental Condition Estimators in the 2-norm.
SIAM Journal on Matrix Analysis and Applications. Roč. 35, č. 1 (2014), s. 174-197. ISSN 0895-4798. E-ISSN 1095-7162
R&D Projects: GA ČR GA13-06684S
Institutional support: RVO:67985807
Keywords : condition number estimation * matrix inverses * incremental condition estimator * incremental norm estimator
Subject RIV: BA - General Mathematics
Impact factor: 1.590, year: 2014

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.
Permanent Link: http://hdl.handle.net/11104/0228778