JUCS - Journal of Universal Computer Science 4(2): 171-177, doi: 10.3217/jucs-004-02-0171
Finding All Solutions of Nonlinear Systems of Equations Using Linear Programming with Guaranteed Accuracy
expand article infoYusuke Nakaya‡, Shin ichi Oishi§
‡ Oishi Lab., Graduate School of Science and Engineering, Waseda Univ., Japan§ Department of Information and Computer Science, School of Science and Engineering, Waseda University, Japan

Corresponding author: Yusuke Nakaya ( nakaya@oishi.info.waseda.ac.jp )

© Yusuke Nakaya, Shin Oishi.
This article is freely available under the J.UCS Open Content License.
Citation: Nakaya Y, Oishi S (1998) Finding All Solutions of Nonlinear Systems of Equations Using Linear Programming with Guaranteed Accuracy. JUCS - Journal of Universal Computer Science 4(2): 171-177. https://doi.org/10.3217/jucs-004-02-0171
Open Access
Abstract
A linear programming-based method is presented for finding all solutions of nonlinear systems of equations with guaranteed accuracy. In this method, a new effective linear programming-based method is used to delete regions in which solutions do not exist. On the other hand, Krawczyk's method is used to find regions in which solutions exist. As an illustrative example, all solutions of the nonlinear system of equations describing equilibrium conditions of the "high polymer liquid system", which is a well-known ill-conditioned system of equations, are identified by the method.
Keywords
Nonlinear Equations, All Solutions, Guaranteed Accuracy, Linear Programming, Krawczyk's Method