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Newton's Method and Generation of a Determinantal Family of Iteration Functions

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Language
LanguageTerm (authority = ISO 639-3:2007); (type = text)
English
Genre (authority = RULIB-FS)
Other
Genre (authority = marcgt)
technical report
PhysicalDescription
InternetMediaType
application/pdf
Extent
7 p.
Note (type = special display note)
Technical report DCS-TR-371
Name (authority = RutgersOrg-School); (type = corporate)
NamePart
School of Arts and Sciences (SAS) (New Brunswick)
Name (authority = RutgersOrg-Department); (type = corporate)
NamePart
Computer Science (New Brunswick)
TypeOfResource
Text
TitleInfo
Title
Newton's Method and Generation of a Determinantal Family of Iteration Functions
Subject (authority = LCSH)
Topic
Newton-Raphson method
Subject (authority = local)
Topic
Rootfinding
Subject (authority = local)
Topic
Polynomial roots
Abstract (type = abstract)
It is well-known that Halley’s method can be obtained by applying Newton’s method to the function f/√ f ′ . Gerlach [3], gives a generalization of this approach, and for each m ≥ 2, recursively defines an iteration function Gm(x) having order m. Kalantari et al. [6], and Kalantari [8] derive and characterize a determinantal family of iteration functions, called the Basic Family, Bm(x), m ≥ 2. In this paper we prove, Gm (x) = Bm (x). On the one hand, this implies that Gm(x) enjoys the previously derived properties of Bm(x), i.e., the closed formula, its efficient computation, an expansion formula which gives its precise asymptotic constant, as well as its multipoint versions. On the other hand, this gives a new insight on the Basic Family and Newton’s method.
Name (type = personal)
NamePart (type = family)
Kalantari
NamePart (type = given)
Bahman
Affiliation
Computer Science (New Brunswick)
Role
RoleTerm (authority = marcrt); (type = text)
author
Name (type = personal)
NamePart (type = family)
Gerlach
NamePart (type = given)
Jürgen
Affiliation
Role
RoleTerm (authority = marcrt); (type = text)
author
OriginInfo
DateCreated (encoding = w3cdtf); (keyDate = yes); (qualifier = exact)
1998-11
Subject (authority = LCSH)
Topic
Roots, Numerical
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/T3280C8M
Genre (authority = ExL-Esploro)
Technical Documentation
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Status
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Technical

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ContentModel
Document
CreatingApplication
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1.4
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GPL Ghostscript 9.07
DateCreated (point = start); (encoding = w3cdtf); (qualifier = exact)
2018-06-06T12:28:38
DateCreated (point = start); (encoding = w3cdtf); (qualifier = exact)
2018-06-06T12:28:38
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Version 8.3.13