About: Local convergence

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In numerical analysis, an iterative method is called locally convergent if the successive approximations produced by the method are guaranteed to converge to a solution when the initial approximation is already close enough to the solution. Iterative methods for nonlinear equations and their systems, such as Newton's method are usually only locally convergent. An iterative method that converges for an arbitrary initial approximation is called globally convergent. Iterative methods for systems of linear equations are usually globally convergent. * v * t * e

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rdf:type	yago:WikicatOptimizationAlgorithmsAndMethods yago:Ability105616246 yago:Abstraction100002137 yago:Act100030358 yago:Activity100407535 yago:Algorithm105847438 yago:Cognition100023271 yago:Event100029378 yago:Know-how105616786 yago:Method105660268 yago:Procedure101023820 yago:PsychologicalFeature100023100 yago:WikicatIterativeMethods yago:YagoPermanentlyLocatedEntity yago:Rule105846932
rdfs:label	Local convergence (en) 局所収束性 (ja)
rdfs:comment	In numerical analysis, an iterative method is called locally convergent if the successive approximations produced by the method are guaranteed to converge to a solution when the initial approximation is already close enough to the solution. Iterative methods for nonlinear equations and their systems, such as Newton's method are usually only locally convergent. An iterative method that converges for an arbitrary initial approximation is called globally convergent. Iterative methods for systems of linear equations are usually globally convergent. * v * t * e (en) 局所収束性（きょくしょしゅうそくせい、英語: locally convergent、局所的収束性）は、数値解析において初期点が最適解に十分に近いときに最適解に十分に収束することが保証された反復法である。ニュートン法のようなおよび非線形方程式系で使用される反復法は一般的に局所収束性だけを満たす。任意の初期点に対して収束する反復法は大域収束性、大域的収束性に分類される。線型方程式系で使用される反復法は一般的に大域収束性を満たす。 (ja)
dct:subject	Iterative methods Optimization algorithms and methods Numerical analysis
Wikipage page ID	16344093 (xsd:integer)
Wikipage revision ID	865949636 (xsd:integer)
Link from a Wikipage to another Wikipage	Nonlinear equation Limit of a sequence Iterative methods Approximation Optimization algorithms and methods Numerical analysis Numerical analysis Iterative method Newton's method Linear equations
sameAs	Local convergence Local convergence Local convergence Local convergence Local convergence
dbp:wikiPageUsesTemplate	dbt:Mathanalysis-stub
has abstract	In numerical analysis, an iterative method is called locally convergent if the successive approximations produced by the method are guaranteed to converge to a solution when the initial approximation is already close enough to the solution. Iterative methods for nonlinear equations and their systems, such as Newton's method are usually only locally convergent. An iterative method that converges for an arbitrary initial approximation is called globally convergent. Iterative methods for systems of linear equations are usually globally convergent. * v * t * e (en) 局所収束性（きょくしょしゅうそくせい、英語: locally convergent、局所的収束性）は、数値解析において初期点が最適解に十分に近いときに最適解に十分に収束することが保証された反復法である。ニュートン法のようなおよび非線形方程式系で使用される反復法は一般的に局所収束性だけを満たす。任意の初期点に対して収束する反復法は大域収束性、大域的収束性に分類される。線型方程式系で使用される反復法は一般的に大域収束性を満たす。 (ja)
prov:wasDerivedFrom	wikipedia-en:Local_convergence?oldid=865949636&ns=0
page length (characters) of wiki page	748 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Local_convergence
is Link from a Wikipage to another Wikipage of	List of numerical analysis topics Gauss–Newton algorithm Global convergence Locally convergent
is Wikipage redirect of	Global convergence Locally convergent
is foaf:primaryTopic of	wikipedia-en:Local_convergence

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