Böttcher, Albrecht ; Potts, Daniel ; Wenzel, David : A probability argument in favor of ignoring small singular values

Author(s):

Böttcher, Albrecht
Potts, Daniel
Wenzel, David

Title:

A probability argument in favor of ignoring small singular values

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 9, 2006

Mathematics Subject Classification:

65F35			[ Matrix norms, conditioning, scaling ]
15A12			[ Conditioning of matrices ]
60H25			[ Random operators and equations ]
65F22			[ Ill-posedness, regularization ]

Abstract:

If the matrix of a square linear system is nonsingular but has very small singular values, then tiny perturbations of the right-hand side may cause drastic changes in the solution. We show that the probability for this to happen is very close to zero if sufficiently many singular values of the matrix are bounded away from zero.

Keywords:

condition number, probability argument, linear system, singular value

Language:

English

Publication time:

5 / 2006