Fixed-point iteration

Fixed-point iteration

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.

Comment
enIn 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.
Depiction
Cosine fixed point.svg
Sierpinski Chaos.gif
Sine fixed point.svg
Has abstract
enIn 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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Fixed-point iteration
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enFixed-point iteration
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algonum.appspot.com/%23fixpoint.picard
wydawnictwa.ptm.org.pl/index.php/antiquitates-mathematicae/article/view/7056/6528
books.google.com/books%3Fid=9Wxk_z9HskAC&pg=PA165
books.google.com/books%3Fid=Kf8TiuXgNYQC
books.google.com/books%3Fid=T2uTAwAAQBAJ
books.google.com/books%3Fid=VKs7Afjkng4C&pg=PA141
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Aitken's delta-squared process
Anderson acceleration
Antiquitates Mathematicae
A-stability
Attractor
Babylonian method
Banach fixed-point theorem
Bellman equation
Bifurcation theory
Category:Fixed-point theorems
Category:Iterative methods
Category:Root-finding algorithms
Cobweb model
Cobweb plot
Colebrook equation
Complete metric space
Complex number
Contraction mapping
Convergence acceleration
Cosine
Cubic convergence
Dense set
Domain of a function
Dottie number
Dynamical system
Dynamic programming
File:Cosine fixed point.svg
File:Sierpinski Chaos.gif
File:Sine fixed point.svg
Fixed point (mathematics)
Fixed-point combinator
Fixed-point theorems
Fractal
Halley's method
Infinite compositions of analytic functions
Iterated function
Iterated function system
Limit (mathematics)
Limit of a sequence
Linear convergence
Linear differential equation
Lipschitz continuity
Logistic map
Lyapunov stable
Markov chain
Metric space
Newton's method
Numerical analysis
Ordinary differential equation
Periodic orbits
Picard–Lindelöf theorem
Price theory
Quadratic convergence
Radian
Real number
Root-finding algorithm
Runge–Kutta method
Sequence
Sierpinski triangle
Square root
Steffensen's method
Strange attractor
SameAs
7iN5
Fikspunktiterasjon
Fixed-point iteration
Fixpunktiteration
Iteração de ponto fixo
Iterazione di punto fisso
m.025zrht
Metoda navadne iteracije
Método del punto fijo
Q1030759
Метод простой итерации
Метод простої ітерації
نقطة ثابتة تكرارية
Subject
Category:Fixed-point theorems
Category:Iterative methods
Category:Root-finding algorithms
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Sine fixed point.svg?width=300
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