Media type: E-Article Title: Finding all solutions of weakly nonlinear equations using the dual simplex method Contributor: Yamamura, Kiyotaka; Tanaka, Katsumasa imprint: Wiley, 2006 Published in: Electronics and Communications in Japan (Part III: Fundamental Electronic Science) Language: English DOI: 10.1002/ecjc.20220 ISSN: 1042-0967; 1520-6440 Keywords: Electrical and Electronic Engineering Origination: Footnote: Description: <jats:title>Abstract</jats:title><jats:p>Recently, efficient algorithms have been proposed for finding all solutions of nonlinear equations using linear programming (LP). These algorithms are based on a simple test (termed the LP test) for nonexistence of a solution to a system of nonlinear equations in a given region. In the LP test, a system of nonlinear equations is transformed into an LP problem by surrounding component nonlinear functions by rectangles or right‐angled triangles. In this paper, an efficient algorithm is proposed for finding all solutions of weakly nonlinear equations, where component nonlinear functions are surrounded by parallelograms and then the dual simplex method is applied to the LP problem. Numerical examples are given to confirm the effectiveness of the proposed algorithm. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 89(7): 1–7, 2006; Published online in Wiley InterScience (<jats:ext-link xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://www.interscience.wiley.com">www.interscience.wiley.com</jats:ext-link>). DOI 10.1002/ecjc.20220</jats:p>