We exhibit a class of nonlinear operators with the property that their iterates converge to their unique fixed points even when computational errors are present. We also show that most (in the sense of the Baire category) elements in an appropriate complete metric space of operators do, in fact, possess this property.
Bibliographical noteFunding Information:
Acknowledgments. A part of the first author’s work on this paper was carried out when he was visiting the Institute of Mathematics of the Technical University of Lódź. The second author was partially supported by the Fund for the Promotion of Research at the Technion and by the Technion VPR Fund — B. and G. Greenberg Research Fund (Ottawa). All three authors are grateful to a referee for a careful reading of the manuscript and for many helpful comments.
- Complete metric space
- Generic property
- Inexact orbit
ASJC Scopus subject areas
- Mathematical Physics
- Statistics, Probability and Uncertainty
- Computational Theory and Mathematics
- Applied Mathematics