An Interval Arithmetic Newton Method for Solving Systems of Nonlinear Equations

Authors

Ronald I. Greenberg, Washington University in St. LouisFollow
Eldon R. Hansen, Lockheed Missiles & Space Company

Document Type

Presentation

Publication Date

4-1982

Publication Title

Illinois State Academy of Science Annual Meeting

Abstract

We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three sub-algorithms. The first is a Gauss-Seidel type step. The second is a real (non-interval) Newton iteration. The third solves the linearized equations by elimination. We explain why each sub-algorithm is desirable and how they fit together to provide solutions in as little as 1/3 to 1/4 the time required by a commonly used method due to Krawczyk.

Comments

The work described in this talk led to the article that can be found at http://ecommons.luc.edu/cs_facpubs/91

Recommended Citation

Greenberg, Ronald I. and Hansen, Eldon R.. An Interval Arithmetic Newton Method for Solving Systems of Nonlinear Equations. Illinois State Academy of Science Annual Meeting, , : , 1982. Retrieved from Loyola eCommons, Computer Science: Faculty Publications and Other Works,

Creative Commons License

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

Copyright Statement

© 1982 The Authors.