Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Journal Article > Item 987654321/58693

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Title:	Balancing the lifting values to improve the numerical stability of polyhedral homotopy continuation methods
Authors:	Li, Tien-yien;Gao, Tan-gan;Verschelde, Jan;Wu, Meng-nien
Contributors:	淡江大學數學學系
Keywords:	Polyhedral homotopies;Path following;Numerical stability;Balancing
Date:	2000-09-01
Issue Date:	2011-10-01 21:03:50 (UTC+8)
Abstract:	Polyhedral homotopy continuation methods exploit the sparsity of polynomial systems so that the number of solution curves to reach all isolated solutions is optimal for generic systems. The numerical stability of tracing solution curves of polyhedral homotopies is mainly determined by the height of the powers of the continuation parameter. To reduce this height, we propose a procedure that operates as an intermediate stage between the mixed-volume computation and the tracing of solution curves. This procedure computes new lifting values of the support of a polynomial system. These values preserve the structure of the mixed-cell configuration obtained from the mixed-volume computation and produce better-balanced powers of the continuation parameter in the polyhedral homotopies.
Relation:	Applied mathematics and computation 114(2-3), pp.233-247
DOI:	10.1016/S0096-3003(99)00115-0
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

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