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Numerical Homotopies for Algebraic S...

Guan, Yun.

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Numerical Homotopies for Algebraic Sets on a Parallel Computer.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Numerical Homotopies for Algebraic Sets on a Parallel Computer./
Author:	Guan, Yun.
Description:	108 p.
Notes:	Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: .
Contained By:	Dissertation Abstracts International72-04B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3446102
ISBN:	9781124499932

Numerical Homotopies for Algebraic Sets on a Parallel Computer.
Guan, Yun.

Numerical Homotopies for Algebraic Sets on a Parallel Computer. - 108 p.

Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: .

Thesis (Ph.D.)--University of Illinois at Chicago, 2010.

PHClab, a MATLAB/Octave interface to PHCpack, provides automatic conversions of the formats for polynomial systems and solutions. It allows the user to access the the functionality of PHCpack within a MATLAB/Octave session. A parallel computation using the combination of PHClab and MPITB for Octave have been conducted for a set of origami equations.

ISBN: 9781124499932Subjects--Topical Terms:

1669109
Applied Mathematics.

Numerical Homotopies for Algebraic Sets on a Parallel Computer.
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020 $a 9781124499932
035 $a (UMI)AAI3446102
035 $a AAI3446102
040 $a UMI $c UMI
100 1 $a Guan, Yun. $3 1675973
245 1 0 $a Numerical Homotopies for Algebraic Sets on a Parallel Computer.
300 $a 108 p.
500 $a Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: .
500 $a Adviser: Jan Verschelde.
502 $a Thesis (Ph.D.)--University of Illinois at Chicago, 2010.
520 $a PHClab, a MATLAB/Octave interface to PHCpack, provides automatic conversions of the formats for polynomial systems and solutions. It allows the user to access the the functionality of PHCpack within a MATLAB/Octave session. A parallel computation using the combination of PHClab and MPITB for Octave have been conducted for a set of origami equations.
520 $a Our implementation of a parallel subsystem-by-subsystem solver provides parallel algorithms to solve a system of polynomial equations by first solving subsets of the system and then intersecting the results. This approach leads to numerical representations of all solution components of a polynomial system. Applications that have all paths converge to regular solutions are selected because we concentrate our discussion on the job scheduling algorithms.
520 $a Numerical data structures for positive dimensional solution sets of polynomial systems are sets of generic points cut out by random planes of complimentary dimension. The linear spaces may be represented either by explicit linear equations or in parametric form. These descriptions are respectively called extrinsic and intrinsic representations. While intrinsic representations lower the cost of the linear algebra operations, we observe worse condition numbers. The local adaptation of intrinsic coordinates can improve the numerical conditioning of sampling algebraic sets, and lead to a better stepsize control.
590 $a School code: 0799.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Computer Science. $3 626642
690 $a 0364
690 $a 0984
710 2 $a University of Illinois at Chicago. $3 1020478
773 0 $t Dissertation Abstracts International $g 72-04B.
790 1 0 $a Verschelde, Jan, $e advisor
790 $a 0799
791 $a Ph.D.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3446102