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Geometric symbolic-numeric methods f...

Wu, Wenyuan.

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Geometric symbolic-numeric methods for differential and algebraic systems.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Geometric symbolic-numeric methods for differential and algebraic systems./
Author:	Wu, Wenyuan.
Description:	195 p.
Notes:	Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1047.
Contained By:	Dissertation Abstracts International69-02B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NR36759
ISBN:	9780494367599

Geometric symbolic-numeric methods for differential and algebraic systems.
Wu, Wenyuan.

Geometric symbolic-numeric methods for differential and algebraic systems. - 195 p.

Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1047.

Thesis (Ph.D.)--The University of Western Ontario (Canada), 2007.

General (e.g. under and over-determined) systems of polynomially nonlinear partial differential equations (PDE) arise frequently in diverse applications. Analyzing such systems requires differentiations and eliminations to detect and include all their integrability conditions. Existing symbolic differential elimination algorithms for this purpose can be prohibitively expensive and only apply to exact systems of PDE and do not stably apply to the approximate systems occurring in applications.

ISBN: 9780494367599Subjects--Topical Terms:

515831
Mathematics.

Geometric symbolic-numeric methods for differential and algebraic systems.
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020 $a 9780494367599
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035 $a AAINR36759
040 $a UMI $c UMI
100 1 $a Wu, Wenyuan. $3 1675839
245 1 0 $a Geometric symbolic-numeric methods for differential and algebraic systems.
300 $a 195 p.
500 $a Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1047.
502 $a Thesis (Ph.D.)--The University of Western Ontario (Canada), 2007.
520 $a General (e.g. under and over-determined) systems of polynomially nonlinear partial differential equations (PDE) arise frequently in diverse applications. Analyzing such systems requires differentiations and eliminations to detect and include all their integrability conditions. Existing symbolic differential elimination algorithms for this purpose can be prohibitively expensive and only apply to exact systems of PDE and do not stably apply to the approximate systems occurring in applications.
520 $a The main contributions of this Thesis are to provide the first practical and stable methods to address the above problems for approximate PDE ; and to establish mathematical foundations for this area. These contributions build on a proposal by Reid et al., to extend tools from Numerical Algebraic Geometry to general systems of PDE in the framework of the geometric theory of PDE (Jet Geometry).
520 $a Differentiating systems yields PDE systems that are always linear in their highest derivatives. Two methods are given to exploit this linearity. One is a hybrid method that applies to exact input systems. The other applies to approximate systems. For a class of PDE appearing in applications, we give an efficient method that only requires differentiations with respect to one independent variable.
520 $a As in Numerical Algebraic Geometry, in Numerical Jet Geometry, the components of PDE are geometrically represented by certain approximate witness points, cut out by intersection of random linear spaces with the components. Such witness points can be efficiently and stably computed by numerical homotopy continuation methods.
520 $a Keywords: Jet Geometry. Involution; Formal Integrability, Cartan Kuranishi Algorithm; Numerical Algebraic Geometry; Homotopy Continuation; Approximate Triangular Decomposition; Polynomial Matrix; Riquier Bases.
590 $a School code: 0784.
650 4 $a Mathematics. $3 515831
690 $a 0405
710 2 $a The University of Western Ontario (Canada). $3 1017622
773 0 $t Dissertation Abstracts International $g 69-02B.
790 $a 0784
791 $a Ph.D.
792 $a 2007
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=NR36759