An Interval Newton Method
Applied Mathematics and Computation
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  in our implementations.
Applied Mathematics and Computation, Volume 12, Issues 2--3, Pages 89--98
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Copyright © 1983 Published by Elsevier Inc.