Interval solution of nonlinear equations using linear programming |
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Authors: | Kiyotaka Yamamura Hitomi Kawata Ai Tokue |
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Institution: | (1) Department of Computer Science, Gunma University, 1-5-1 Tenjin-cho, 376 Kiryu, Japan |
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Abstract: | A new computational test is proposed for nonexistence of a solution to a system of nonlinear equations in a convex polyhedral
regionX. The basic idea proposed here is to formulate a linear programming problem whose feasible region contains all solutions inX. Therefore, if the feasible region is empty (which can be easily checked by Phase I of the simplex method), then the system
of nonlinear equations has no solution inX. The linear programming problem is formulated by surrounding the component nonlinear functions by rectangles using interval
extensions. This test is much more powerful than the conventional test if the system of nonlinear equations consists of many
linear terms and a relatively small number of nonlinear terms. By introducing the proposed test to interval analysis, all
solutions of nonlinear equations can be found very efficently.
This work was partially supported by the Japanese Ministry of Education. |
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Keywords: | 65H10 65G10 |
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