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Computation of all solutions to a system of polynomial equations

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Abstract

This paper proposes a homotopy continuation method for approximating all solutions to a system of polynomial equations in several complex variables. The method is based on piecewise linear approximation and complementarity theory. It utilizes a skilful artificial map and two copies of the triangulationJ 3 with continuous refinement of grid size to increase the computational efficiency and to avoid the necessity of determining the grid size a priori. Some computational results are also reported.

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Authors and Affiliations

  1. Department of Information Sciences, Tokyo Institute of Technology, Meguro, 152, Tokyo, Japan

    Masakazu Kojima

  2. Department of Systems Science, Graduate School of Science and Engineering, Tokyo Institute of Technology, Midori-ku, 227, Yokohama, Japan

    Shinji Mizuno

Authors
  1. Masakazu Kojima
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  2. Shinji Mizuno
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Kojima, M., Mizuno, S. Computation of all solutions to a system of polynomial equations. Mathematical Programming 25, 131–157 (1983). https://doi.org/10.1007/BF02591768

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  • DOI: https://doi.org/10.1007/BF02591768

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