About: Fixed-point iteration

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In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space.

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rdf:type	yago:WikicatRoot-findingAlgorithms 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	نقطة ثابتة تكرارية (ar) Fixpunktiteration (de) Método del punto fijo (es) Fixed-point iteration (en) Iterazione di punto fisso (it) Метод простой итерации (ru) Iteração de ponto fixo (pt) Метод простої ітерації (uk)
rdfs:comment	نقطة ثابتة تكرارية (بالإنجليزية: Fixed-point iteration)‏ تستخدم هذه الطريقة التكرارية لحل المعادلات و تتميز بأنها لا تتطلب حساب قيم أي مشتقات كما في طريقة نيوتن حيث لحل المعادلة نحتاج إلى حساب قيمة مشتقة الدالة عند كل خطوة. (ar) El método del punto fijo es un método iterativo que permite resolver sistemas de ecuaciones no necesariamente lineales. En particular se puede utilizar para determinar raíces de una función de la forma , siempre y cuando se cumplan los criterios de convergencia. (es) In numerical analysis, fixed-point iteration is a method of computing fixed points of a function. More specifically, given a function defined on the real numbers with real values and given a point in the domain of , the fixed-point iteration is which gives rise to the sequence of iterated function applications which is hoped to converge to a point . If is continuous, then one can prove that the obtained is a fixed point of , i.e., More generally, the function can be defined on any metric space with values in that same space. (en) In analisi numerica, l'iterazione di punto fisso o iterazione funzionale è un metodo per trovare le radici di una funzione, ovvero per risolvere un'equazione nella forma . Se sono due funzioni tali che , allora si ha se e solo se , cioè è radice di se e solo se è punto fisso di . Il metodo consiste nel risolvere l'equazione dove la generica espressione di è: Si vede quindi che , ovvero la funzione di iterazione, può essere scelta in vari modi. Ad esempio se si può scegliere: La soluzione si approssima (scelto un punto iniziale) con la successione: (it) Em análise numérica, iteração de ponto fixo é um método de se calcular pontos fixos de funções. Ponto fixo de dada função é o número que quando aplicado na função resulta nele mesmo, i.e. . Dada uma aproximação inicial para , o método consiste em iterar sucessivamente a função dada sobre . Ou seja, constrói-se a sequência sendo cada uma nova aproximação do ponto fixo . Uma importante aplicação deste método aparece no cálculo numérico de soluções de equações de uma variável real. (pt) Метод простой итерации — один из простейших численных методов решения уравнений. Метод основан на принципе сжимающего отображения, который применительно к численным методам в общем виде также может называться методом простой итерации или методом последовательных приближений. В частности, для систем линейных алгебраических уравнений существует аналогичный метод итерации. (ru) Метод простої ітерації - метод обчислення нерухомої точки функції. (uk) Eine Fixpunktiteration (oder auch ein Fixpunktverfahren) ist in der Mathematik ein numerisches Verfahren zur näherungsweisen Bestimmung von Lösungen einer Gleichung oder eines Gleichungssystems. Die Gleichung muss dazu zuerst in eine Fixpunktgleichung, also in eine Gleichung der Form (de)
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dct:subject	Iterative methods Fixed-point theorems Root-finding algorithms
Wikipage page ID	7344320 (xsd:integer)
Wikipage revision ID	1119689321 (xsd:integer)
Link from a Wikipage to another Wikipage	Bellman equation Babylonian method Root-finding algorithm Convergence acceleration Dottie number Dynamical system Limit of a sequence Quadratic convergence Complex number Anderson acceleration Iterative methods Contraction mapping Cosine Limit (mathematics) Linear differential equation Lipschitz continuity Logistic map Lyapunov stable Steffensen's method Strange attractor Complete metric space Dense set Halley's method Domain of a function Cubic convergence Aitken's delta-squared process Dynamic programming Fixed point (mathematics) Banach fixed-point theorem Numerical analysis Fractal Iterated function system Colebrook equation Attractor Fixed-point theorems Iterated function Root-finding algorithms Bifurcation theory Cobweb model Cobweb plot Picard–Lindelöf theorem Square root Infinite compositions of analytic functions Metric space Newton's method Ordinary differential equation Radian Real number Sequence Markov chain Fixed-point combinator Fixed-point theorems Sierpiński triangle Runge–Kutta method Linear convergence A-stability Periodic orbits Price theory dbr:Antiquitates_Mathematicae

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