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Mixed volume and total degree.

Zhang, Ying.

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Mixed volume and total degree.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Mixed volume and total degree./
Author:	Zhang, Ying.
Description:	65 p.
Notes:	Source: Dissertation Abstracts International, Volume: 69-10, Section: B, page: 6151.
Contained By:	Dissertation Abstracts International69-10B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3332052
ISBN:	9780549844211

Mixed volume and total degree.
Zhang, Ying.

Mixed volume and total degree. - 65 p.

Source: Dissertation Abstracts International, Volume: 69-10, Section: B, page: 6151.

Thesis (Ph.D.)--Michigan State University, 2008.

This thesis focuses on the study of solving several extensible benchmark polynomial systems by homotopy continuation methods. By establishing the relationship between their mixed volume and total degree, we find that for most of those systems the difference between their mixed volume and total degree is very minimal. Consequently, those systems should be solved by the classical linear homotopy method rather than the polyhedral homotopy method, although in general the polyhedral homotopy method is the typical choice for solving sparse systems. Furthermore, by restricting to the classical linear homotopy on solving those systems, we may take the special structure of the systems into account for solving the systems efficiently. This precious aspect of the classical linear homotopy does not seem to exist in the polyhedral homotopy method.

ISBN: 9780549844211Subjects--Topical Terms:

515831
Mathematics.

Mixed volume and total degree.
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020 $a 9780549844211
035 $a (UMI)AAI3332052
035 $a AAI3332052
040 $a UMI $c UMI
100 1 $a Zhang, Ying. $3 1035770
245 1 0 $a Mixed volume and total degree.
300 $a 65 p.
500 $a Source: Dissertation Abstracts International, Volume: 69-10, Section: B, page: 6151.
500 $a Adviser: Tien-Yien Li.
502 $a Thesis (Ph.D.)--Michigan State University, 2008.
520 $a This thesis focuses on the study of solving several extensible benchmark polynomial systems by homotopy continuation methods. By establishing the relationship between their mixed volume and total degree, we find that for most of those systems the difference between their mixed volume and total degree is very minimal. Consequently, those systems should be solved by the classical linear homotopy method rather than the polyhedral homotopy method, although in general the polyhedral homotopy method is the typical choice for solving sparse systems. Furthermore, by restricting to the classical linear homotopy on solving those systems, we may take the special structure of the systems into account for solving the systems efficiently. This precious aspect of the classical linear homotopy does not seem to exist in the polyhedral homotopy method.
590 $a School code: 0128.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a Michigan State University. $3 676168
773 0 $t Dissertation Abstracts International $g 69-10B.
790 1 0 $a Li, Tien-Yien, $e advisor
790 $a 0128
791 $a Ph.D.
792 $a 2008
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3332052