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A computational comparison of the first nine members of a determinantal family of rootfinding methods

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LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Genre (authority = RULIB-FS)
Other
Genre (authority = marcgt)
technical report
PhysicalDescription
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application/pdf
Extent
1 online resource (8 pages)
Note (type = special display note)
Technical report DCS-TR-375
Name (type = corporate); (authority = RutgersOrg-School)
NamePart
School of Arts and Sciences (SAS) (New Brunswick)
Name (type = corporate); (authority = RutgersOrg-Department)
NamePart
Computer Science (New Brunswick)
TypeOfResource
Text
TitleInfo
Title
A computational comparison of the first nine members of a determinantal family of rootfinding methods
Subject (authority = local)
Topic
Polynomial zeros
Subject (authority = local)
Topic
Order of convergence
Abstract (type = abstract)
For each natural number m greater than one, and each natural number k less than or equal to m, there exists a rootfinding iteration function, B (k) m defined as the ratio of two determinants that depend on the first m − k derivatives of the given function. This infinite family is derived in [4] and its order of convergence is analyzed in [5]. In this paper we give a computational study of the first nine rootfinding methods. These include Newton, secant, and Halley methods. Our computational results with polynomials of degree up to 30 reveal that for small degree polynomials B (k−1) m is more efficient than B (k) m , but as the degree increases, B (k) m becomes more efficient than B (k−1) m . The most efficient of the nine methods is B (4) 4, having theoretical order of convergence equal to 1.927. Newton’s method which is often viewed as the method of choice is in fact the least efficient method.
Name (type = personal)
NamePart (type = family)
Kalantari
NamePart (type = given)
Bahman
Affiliation
Computer Science (New Brunswick)
Role
RoleTerm (type = text); (authority = marcrt)
author
Name (type = personal)
NamePart (type = family)
Park
NamePart (type = given)
Seungyoung
Affiliation
Computer Science (New Brunswick)
Role
RoleTerm (type = text); (authority = marcrt)
author
OriginInfo
DateCreated (encoding = w3cdtf); (qualifier = exact); (keyDate = yes)
1998-12
RelatedItem (type = host)
TitleInfo
Title
Computer Science (New Brunswick)
Identifier (type = local)
rucore21032500001
Location
PhysicalLocation (authority = marcorg); (displayLabel = Rutgers, The State University of New Jersey)
NjNbRU
Identifier (type = doi)
doi:10.7282/t3-3440-wz98
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This Item is protected by copyright and/or related rights.You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use.For other uses you need to obtain permission from the rights-holder(s).
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Copyright protected
Availability
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Open
Reason
Permission or license
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Technical

RULTechMD (ID = TECHNICAL1)
ContentModel
Document
CreatingApplication
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1.4
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GPL Ghostscript 9.07
DateCreated (point = start); (encoding = w3cdtf); (qualifier = exact)
2018-06-06T12:28:43
DateCreated (point = start); (encoding = w3cdtf); (qualifier = exact)
2018-06-06T12:28:43
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