Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

On measures of ill-conditioning for nonlinear equations


Author: Werner C. Rheinboldt
Journal: Math. Comp. 30 (1976), 104-111
MSC: Primary 65J05
MathSciNet review: 0400702
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {x^\ast}$ be a solution of the nonlinear equation $ Fx = b$ on a normed linear space and $ {y^\ast}$ that of a perturbed equation $ Gx = c$. Estimates for the relativized error between $ {x^\ast}$ and $ {y^\ast}$ are derived which extend a known estimate for the corresponding matrix case. The condition number of F depends now also on the domain, and special considerations are needed to determine the existence of the solution of the perturbed equation. For differentiable F, when the domain shrinks to a point, the condition number of F is shown to reduce to that of the derivative at that point.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65J05

Retrieve articles in all journals with MSC: 65J05


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1976-0400702-1
PII: S 0025-5718(1976)0400702-1
Article copyright: © Copyright 1976 American Mathematical Society