Document Type
Article
Publication Date
5-1983
Publication Title
Applied Mathematics and Computation
Volume
12
Issue
2-3
Pages
89-98
Publisher Name
Elsevier
Abstract
We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three subalgorithms. The first is a Gauss-Seidel-type step. The second is a real (noninterval) Newton iteration. The third solves the linearized equations by elimination. We explain why each subalgorithm is desirable and how they fit together to provide solutions in as little as one-third or one-quarter the time required by Krawczyk's method [7] in our implementations.
Recommended Citation
Hansen, E R. and Greenberg, R I.. An Interval Newton Method. Applied Mathematics and Computation, 12, 2-3: 89-98, 1983. Retrieved from Loyola eCommons, Computer Science: Faculty Publications and Other Works, http://dx.doi.org/10.1016/0096-3003(83)90001-2
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Copyright Statement
Copyright © 1983 Published by Elsevier Inc.
Included in
Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons
Comments
Author Posting © Elsevier Inc, 1983. This is the author's version of the work. It is posted here by permission of the Elsevier Inc for personal use, not for redistribution. The definitive version was published in Applied Mathematics and Computation, Vol. 12, Iss. 2-3, May 1989. http://dx.doi.org/10.1016/0096-3003(83)90001-2
Presentation slides for a talk on this subject can be found at http://ecommons.luc.edu/cs_facpubs/152