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An experimental study of the triangle algorithm with emphasis on solving a linear system

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TitleInfo
Title
An experimental study of the triangle algorithm with emphasis on solving a linear system
Name (type = personal)
NamePart (type = family)
Shen
NamePart (type = given)
Hao
NamePart (type = date)
1987-
DisplayForm
Hao Shen
Role
RoleTerm (authority = RULIB)
author
Name (type = personal)
NamePart (type = family)
Kalantari
NamePart (type = given)
Bahama
DisplayForm
Bahama Kalantari
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
chair
Name (type = personal)
NamePart (type = family)
Richter
NamePart (type = given)
Gerard
DisplayForm
Gerard Richter
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = personal)
NamePart (type = family)
Saraf
NamePart (type = given)
Shubhangi
DisplayForm
Shubhangi Saraf
Affiliation
Advisory Committee
Role
RoleTerm (authority = RULIB)
internal member
Name (type = corporate)
NamePart
Rutgers University
Role
RoleTerm (authority = RULIB)
degree grantor
Name (type = corporate)
NamePart
Graduate School - New Brunswick
Role
RoleTerm (authority = RULIB)
school
TypeOfResource
Text
Genre (authority = marcgt)
theses
OriginInfo
DateCreated (encoding = w3cdtf); (qualifier = exact)
2015
DateOther (qualifier = exact); (type = degree)
2015-01
CopyrightDate (encoding = w3cdtf); (qualifier = exact)
2015
Place
PlaceTerm (type = code)
xx
Language
LanguageTerm (authority = ISO639-2b); (type = code)
eng
Abstract (type = abstract)
The triangle algorithm, Kalantari [4], is designed to solve the convex hull membership problem. It can also solve LP, and as shown in Kalantari[1] solve a square linear system. In this thesis we carry out some experimentation with the triangle algorithm both for solving convex hull problem and a linear system, however, with more emphasis on the latter problem. We first tested the triangle algorithm on the convex hull problem and made comparison with the Frank-Wolfe algorithm. The triangle algorithm outperformed the Frank-Wolfe for large scale problems, up to 10,000 points in dimensions up to 500. The triangle algorithm takes fewer iterations than the Frank-Wolfe algorithm. For linear systems, we implemented the incremental version of the triangle algorithm in [1] and made some comparison with SOR and Gauss-Seidel methods for systems of dimension up to 1000. The triangle algorithm is more efficient than these algorithms taking fewer iterations. We also tested the triangle algorithm for solving the PageRank matrix by converting it into a convex hull membership problem. We solved the problem in dimensions ranging from 200 to 2200. We made comparisons with the power method. The triangle algorithm took less iterations to reach the same accuracy. Additionally, we tested a large scale PageRank matrix problem of size of 281,903 due to S. Kamvar. Surprisingly, the triangle algorithm took only 1 iteration to obtain a solution with the accuracy of $10^{-10}$.
Subject (authority = RUETD)
Topic
Computer Science
Subject (authority = ETD-LCSH)
Topic
Algorithms
Subject (authority = ETD-LCSH)
Topic
Linear systems
RelatedItem (type = host)
TitleInfo
Title
Rutgers University Electronic Theses and Dissertations
Identifier (type = RULIB)
ETD
Identifier
ETD_6075
PhysicalDescription
Form (authority = gmd)
electronic resource
InternetMediaType
application/pdf
InternetMediaType
text/xml
Extent
1 online resource (ix, 64 p. : ill.)
Note (type = degree)
M.S.
Note (type = bibliography)
Includes bibliographical references
Note (type = statement of responsibility)
by Hao Shen
RelatedItem (type = host)
TitleInfo
Title
Graduate School - New Brunswick Electronic Theses and Dissertations
Identifier (type = local)
rucore19991600001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/T3F191F4
Genre (authority = ExL-Esploro)
ETD graduate
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Rights

RightsDeclaration (ID = rulibRdec0006)
The author owns the copyright to this work.
RightsHolder (type = personal)
Name
FamilyName
Shen
GivenName
Hao
Role
Copyright Holder
RightsEvent
Type
Permission or license
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2015-01-05 23:27:19
AssociatedEntity
Name
Hao Shen
Role
Copyright holder
Affiliation
Rutgers University. Graduate School - New Brunswick
AssociatedObject
Type
License
Name
Author Agreement License
Detail
I hereby grant to the Rutgers University Libraries and to my school the non-exclusive right to archive, reproduce and distribute my thesis or dissertation, in whole or in part, and/or my abstract, in whole or in part, in and from an electronic format, subject to the release date subsequently stipulated in this submittal form and approved by my school. I represent and stipulate that the thesis or dissertation and its abstract are my original work, that they do not infringe or violate any rights of others, and that I make these grants as the sole owner of the rights to my thesis or dissertation and its abstract. I represent that I have obtained written permissions, when necessary, from the owner(s) of each third party copyrighted matter to be included in my thesis or dissertation and will supply copies of such upon request by my school. I acknowledge that RU ETD and my school will not distribute my thesis or dissertation or its abstract if, in their reasonable judgment, they believe all such rights have not been secured. I acknowledge that I retain ownership rights to the copyright of my work. I also retain the right to use all or part of this thesis or dissertation in future works, such as articles or books.
RightsEvent
DateTime (encoding = w3cdtf); (qualifier = exact); (point = start)
2015-01-31
DateTime (encoding = w3cdtf); (qualifier = exact); (point = end)
2015-08-02
Type
Embargo
Detail
Access to this PDF has been restricted at the author's request. It will be publicly available after August 2nd, 2015.
Copyright
Status
Copyright protected
Availability
Status
Open
Reason
Permission or license
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ContentModel
ETD
OperatingSystem (VERSION = 5.1)
windows xp
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