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A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems

Author

Listed:
  • Xiaojie Dou

    (College of Science, Civil Aviation University of China, Tianjin 300300, China)

  • Jin-San Cheng

    (KLMM, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China)

Abstract

In this paper, by transforming the given over-determined system into a square system, we prove a necessary and sufficient condition to certify the simple real zeros of the over-determined system by certifying the simple real zeros of the square system. After certifying a simple real zero of the related square system with the interval methods, we assert that the certified zero is a local minimum of sum of squares of the input polynomials. If the value of sum of squares of the input polynomials at the certified zero is equal to zero, it is a zero of the input system. As an application, we also consider the heuristic verification of isolated zeros of polynomial systems and their multiplicity structures.

Suggested Citation

  • Xiaojie Dou & Jin-San Cheng, 2018. "A Heuristic Method for Certifying Isolated Zeros of Polynomial Systems," Mathematics, MDPI, vol. 6(9), pages 1-18, September.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:9:p:166-:d:169078
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