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Parallel implementation of polyhedra...

Zhuang, Yan.

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Parallel implementation of polyhedral homotopy methods.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Parallel implementation of polyhedral homotopy methods./
Author:	Zhuang, Yan.
Description:	90 p.
Notes:	Source: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4533.
Contained By:	Dissertation Abstracts International68-07B.
Subject:	Mathematics. -
Online resource:	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.
LDR:01962nam 2200301 4500 001 1397024
005 20110705104705.5
008 130515s2007 ||||||||||||||||| ||eng d
020 $a 9780549148616
035 $a (UMI)AAI3274163
035 $a AAI3274163
040 $a UMI $c UMI
100 1 $a Zhuang, Yan. $3 1675837
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.
650 4 $a Mathematics. $3 515831
650 4 $a Computer Science. $3 626642
690 $a 0405
690 $a 0984
710 2 $a University of Illinois at Chicago. $3 1020478
773 0 $t Dissertation Abstracts International $g 68-07B.
790 1 0 $a Verschelde, Jan, $e advisor
790 $a 0799
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3274163