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Parallel implementation of polyhedra...

Zhuang, Yan.

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Parallel implementation of polyhedral homotopy methods.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Parallel implementation of polyhedral homotopy methods./
作者:	Zhuang, Yan.
面頁冊數:	90 p.
附註:	Source: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4533.
Contained By:	Dissertation Abstracts International68-07B.
標題:	Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3274163
ISBN:	9780549148616

Parallel implementation of polyhedral homotopy methods.
Zhuang, Yan.

Parallel implementation of polyhedral homotopy methods. - 90 p.

Source: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4533.

Thesis (Ph.D.)--University of Illinois at Chicago, 2007.

Homotopy continuation methods to compute numerical approximations to all isolated solutions of a polynomial system are known as "pleasingly parallel", i.e.: because of their low communication overhead, these methods scale very well for a large number of processors. Because so many important problems remain unsolved mainly due to their intrinsic computational complexity, it would be embarrassing not to develop parallel implementations of polynomial homotopy continuation methods.

ISBN: 9780549148616Subjects--Topical Terms:

515831
Mathematics.

Parallel implementation of polyhedral homotopy methods.
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245 1 0 $a Parallel implementation of polyhedral homotopy methods.
300 $a 90 p.
500 $a Source: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4533.
500 $a Adviser: Jan Verschelde.
502 $a Thesis (Ph.D.)--University of Illinois at Chicago, 2007.
520 $a Homotopy continuation methods to compute numerical approximations to all isolated solutions of a polynomial system are known as "pleasingly parallel", i.e.: because of their low communication overhead, these methods scale very well for a large number of processors. Because so many important problems remain unsolved mainly due to their intrinsic computational complexity, it would be embarrassing not to develop parallel implementations of polynomial homotopy continuation methods.
520 $a "Parallel PHCpack", is a project which started a couple of years ago developed by my advisor Jan Verschelde and his student Yusong Wang (parallel pieri homotopy), and which continues with Anton Leykin (parallel irreducible decomposition).
520 $a The focus of this thesis is the development of "parallel PHCpack". For sparse polynomial systems, polyhedral methods give efficient homotopy algorithms. The polyhedral homotopy methods run in three stages: (1) compute the mixed volume; (2) solve a random coefficient start system; (3) track solution paths to solve the target system.
590 $a School code: 0799.
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