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	Computing the optimal partition of variables in multi-homogeneous homotopy methods
	Liang, H ; Bai, FS ; Shi, LY
	2010-05-06 ; 2010-05-06
关键词	multi-homogenous Bezout number variable partitions Markov chain global optimization POLYNOMIAL SYSTEMS BEZOUT NUMBER Mathematics, Applied
中文摘要	The multi-homogenous homotopy continuation method is one of the most efficient approaches in finding all isolated solutions of polynomial systems. A different partition of variables leads to a different homotopy system. The homotopy using the optimal partition of variables reduces the computational cost in curve following to the minimum. However, finding the optimal variable partition is likely an NP hard problem. An approximate algorithm is introduced in this paper to avoid exhaustive search in finding the (approximate) optimal variable partition. The global convergence of this algorithm is proved with Markov chain theory. Numerical comparisons with algorithms existed show the efficiency of the new method. (c) 2004 Elsevier Inc. All rights reserved.
语种	英语 ; 英语
出版者	ELSEVIER SCIENCE INC ; NEW YORK ; 360 PARK AVE SOUTH, NEW YORK, NY 10010-1710 USA
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/14010]
专题	清华大学
推荐引用方式 GB/T 7714	Liang, H,Bai, FS,Shi, LY. Computing the optimal partition of variables in multi-homogeneous homotopy methods[J],2010, 2010.
APA	Liang, H,Bai, FS,&Shi, LY.(2010).Computing the optimal partition of variables in multi-homogeneous homotopy methods..
MLA	Liang, H,et al."Computing the optimal partition of variables in multi-homogeneous homotopy methods".(2010).

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