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Avoiding Singularities During Homoto...

Hodges, Timothy E.

Avoiding Singularities During Homotopy Continuation.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Avoiding Singularities During Homotopy Continuation./
Author:	Hodges, Timothy E.
Description:	1 online resource (51 pages)
Notes:	Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
Contained By:	Dissertation Abstracts International78-11B(E).
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9781369868487

Avoiding Singularities During Homotopy Continuation.
Hodges, Timothy E.

Avoiding Singularities During Homotopy Continuation. - 1 online resource (51 pages)

Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

In numerical algebraic geometry, the goal is to find solutions to a polynomial system F(x1, x2,...xn). This is done through a process called homotopy continuation. During this process, it is possible to encounter areas of ill-conditioning. These areas can cause failure of homotopy continuation or an increase in run time. In this thesis, we formalize where these areas of ill-conditioning can happen, and give a novel method for avoiding them. In addition, future work and possible improvements to the method are proposed. We also report on related developments in the Bertini software package. In addition, we discuss new infrastructure and heuristics for tuning configurations during homotopy continuation.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369868487Subjects--Topical Terms:

527692
Mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Avoiding Singularities During Homotopy Continuation.
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008 190606s2017 xx obm 000 0 eng d
020 $a 9781369868487
035 $a (MiAaPQ)AAI10263163
035 $a (MiAaPQ)colostate:14125
035 $a AAI10263163
040 $a MiAaPQ $b eng $c MiAaPQ
099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Hodges, Timothy E. $3 1180658
245 1 0 $a Avoiding Singularities During Homotopy Continuation.
264 0 $c 2017
300 $a 1 online resource (51 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Dissertation Abstracts International, Volume: 78-11(E), Section: B.
500 $a Adviser: Daniel J. Bates.
502 $a Thesis (Ph.D.) $c Colorado State University $d 2017.
504 $a Includes bibliographical references
520 $a In numerical algebraic geometry, the goal is to find solutions to a polynomial system F(x1, x2,...xn). This is done through a process called homotopy continuation. During this process, it is possible to encounter areas of ill-conditioning. These areas can cause failure of homotopy continuation or an increase in run time. In this thesis, we formalize where these areas of ill-conditioning can happen, and give a novel method for avoiding them. In addition, future work and possible improvements to the method are proposed. We also report on related developments in the Bertini software package. In addition, we discuss new infrastructure and heuristics for tuning configurations during homotopy continuation.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Mathematics. $3 527692
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0405
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Colorado State University. $b Mathematics. $3 1180659
773 0 $t Dissertation Abstracts International $g 78-11B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10263163 $z click for full text (PQDT)

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