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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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Solving deficient polynomial systems with homotopies which keep the subschemes at infinity invariant
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by T. Y. Li and Xiao Shen Wang PDF
Math. Comp. 56 (1991), 693-710 Request permission

Abstract:

By a deficient polynomial system of n polynomial equations in n unknowns we mean a system that has fewer solutions than that predicted by the total degree, or the Bézout number, of the system. If the system is m-homogeneous, the Bézout number can be considerably reduced. In this paper, we introduce a homotopy for numerically determining all isolated solutions of deficient m-homogeneous systems. The initial polynomial system Q is chosen which keeps the subschemes of $H(x,t) = (1 - t)aQ(x) + tP(x)$ at infinity invariant when t varies in [0, 1).
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Math. Comp. 56 (1991), 693-710
  • MSC: Primary 65H10; Secondary 65H20
  • DOI: https://doi.org/10.1090/S0025-5718-1991-1066835-2
  • MathSciNet review: 1066835