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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Minimizing multi-homogeneous Bézout numbers by a local search method
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by Tiejun Li and Fengshan Bai PDF
Math. Comp. 70 (2001), 767-787 Request permission

Abstract:

Consider the multi-homogeneous homotopy continuation method for solving a system of polynomial equations. For any partition of variables, the multi-homogeneous Bézout number bounds the number of isolated solution curves one has to follow in the method. This paper presents a local search method for finding a partition of variables with minimal multi-homogeneous Bézout number. As with any other local search method, it may give a local minimum rather than the minimum over all possible homogenizations. Numerical examples show the efficiency of this local search method.
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Additional Information
  • Tiejun Li
  • Affiliation: School of Mathematical Sciences, Peking University, Beijing, P. R. China
  • Fengshan Bai
  • Affiliation: Department of Mathematics, Tsinghua University, Beijing, 100084, P. R. China
  • Email: fbai@math.tsinghua.edu.cn
  • Received by editor(s): September 18, 1998
  • Published electronically: October 18, 2000
  • Additional Notes: Supported by National Science Foundation of China G19871047 and National Key Basic Research Special Fund G1998020306.
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 767-787
  • MSC (2000): Primary 65H10
  • DOI: https://doi.org/10.1090/S0025-5718-00-01303-X
  • MathSciNet review: 1813146