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An Interval Arithmetic Newton Method For Solving Systems Of Nonlinear Equations, Ronald I. Greenberg, Eldon R. Hansen
An Interval Arithmetic Newton Method For Solving Systems Of Nonlinear Equations, Ronald I. Greenberg, Eldon R. Hansen
Ronald Greenberg
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.