TY  - JOUR
T1  - On Incremental Condition Estimators in the 2-Norm
A1  - Duintjer Tebbens, Jurjen
A1  - Tůma, Miroslav
JA  - SIAM. J. Matrix Anal. & Appl.
Y1  - 2014
VL  - 35
IS  - 1
SP  - 174
EP  - 197
M2  - doi: 10.1137/130922872
N2  - 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 V¨omel,
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 V¨omel when appropriately applied
to both the triangular matrix itself and its inverse. This leads to a highly accurate incremental condition number
estimator.
M1  - Preprint project = NCMM
M1  - Preprint year = 2013
M1  - Preprint number = 15
M1  - Preprint ID = NCMM/2013/15
ER  -