Abstract.
The reliability of polyhedral homotopy continuation methods for solving a polynomial system becomes increasingly important as the dimension of the polynomial system increases. High powers of the homotopy continuation parameter t and ill-conditioned Jacobian matrices encountered in tracing of homotopy paths affect the numerical stability. We present modified homotopy functions with a new homotopy continuation parameter s and various scaling strategies to enhance the numerical stability. Advantages of employing the new homotopy parameter s are discussed. Numerical results are included to illustrate the improved performance of the presented techniques.
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A considerable part of this work was conducted while this author was visiting Tokyo Institute of Technology. Research supported by Kosef R004-000-2001-00200.
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Kim, S., Kojima, M. Numerical Stability of Path Tracing in Polyhedral Homotopy Continuation Methods. Computing 73, 329–348 (2004). https://doi.org/10.1007/s00607-004-0070-6
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DOI: https://doi.org/10.1007/s00607-004-0070-6