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Title: Symbolic homotopy construction
Authors: Verschelde, Jan ×
Cools, Ronald #
Issue Date: 1993
Publisher: Springer verlag
Series Title: Applicable algebra in engineering communication and computing vol:4 issue:3 pages:169-183
Abstract: The classical Theorem of Bezout yields an upper bound for the number of finite solutions to a given polynomial system, but is very often too large to be useful for the construction of a start system, for the solution of a polynomial system by means of homotopy continuation. The BKK bound gives a much lower upper bound for the number of solutions, but unfortunately, constructing a start system based on this bound seems as hard as solving the original given polynomial system. This paper presents a way for computing an upper bound together with the construction of a start system. The first computation is performed symbolically. Due to this symbolic computation, the constructed start system can be solved numerically more efficiently. The paper generalizes current approaches for homotopy construction towards the BKK bound.
URI: 
ISSN: 0938-1279
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Numerical Analysis and Applied Mathematics Section
× corresponding author
# (joint) last author

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