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.

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

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.

HansenG1983talk.pdf (6160 kB)
An Interval Arithmetic Newton Method for Solving Systems of Nonlinear Equations" presented by Ronald I. Greenberg at the Illinois State Academy of Science Annual Meeting, Decatur, IL, April 1982

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