Convergence of recursive functions on computers

A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions {fn} is convergent on a metric space I ⊆ ℝ, then it is possible to observe this behaviour on the set 𝔻 ⊂ ℚ of all numbers represented in a computer. However,...

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Vydáno v:Journal of engineering (Stevenage, England) Ročník 2014; číslo 10; s. 560 - 562
Hlavní autor: Nepomuceno, Erivelton Geraldo
Médium: Journal Article
Jazyk:angličtina
Vydáno: The Institution of Engineering and Technology 01.10.2014
Wiley
Témata:
convergence of numerical methods
convergent function sequence
metric space
numerical computation
recursive function convergence
recursive function fixed points
recursive functions
set theory
convergent function sequence
metric space
numerical computation
recursive functions
convergence of numerical methods
set theory
recursive function fixed points
recursive function convergence
ISSN:2051-3305, 2051-3305
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Abstract A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions {fn} is convergent on a metric space I ⊆ ℝ, then it is possible to observe this behaviour on the set 𝔻 ⊂ ℚ of all numbers represented in a computer. However, as 𝔻 is not complete, the representation of fn on 𝔻 is subject to an error. Then fn and fm are considered equal when its differences computed on 𝔻 are equal or lower than the sum of error of each fn and fm. An example is given to illustrate the use of the theorem.
AbstractList A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions {f(n)} is convergent on a metric space I ⊆ ℝ, then it is possible to observe this behaviour on the set 𝔻 ⊂ ℚ of all numbers represented in a computer. However, as 𝔻 is not complete, the representation of f(n) on 𝔻 is subject to an error. Then f(n) and f(m) are considered equal when its differences computed on 𝔻 are equal or lower than the sum of error of each f(n) and f(m). An example is given to illustrate the use of the theorem.
A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions {fn } is convergent on a metric space I ⊆ ℝ, then it is possible to observe this behaviour on the set 𝔻 ⊂ ℚ of all numbers represented in a computer. However, as 𝔻 is not complete, the representation of fn on 𝔻 is subject to an error. Then fn and fm are considered equal when its differences computed on 𝔻 are equal or lower than the sum of error of each fn and fm. An example is given to illustrate the use of the theorem.
A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions { f n } is convergent on a metric space I ⊆ ℝ, then it is possible to observe this behaviour on the set ⊂ ℚ of all numbers represented in a computer. However, as is not complete, the representation of f n on is subject to an error. Then f n and f m are considered equal when its differences computed on are equal or lower than the sum of error of each f n and f m . An example is given to illustrate the use of the theorem.
Author Nepomuceno, Erivelton Geraldo
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  organization: 2Model and Control Group, Department of Electrical Engineering, Federal University of São João del-Rei, São João del-Rei, Brazil
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10.1038/261459a0
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10.1017/CBO9780511626296
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10.1007/BF02703801
10.1007/s11071-013-1007-4
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Issue 10
Keywords convergent function sequence
metric space
numerical computation
recursive functions
convergence of numerical methods
set theory
recursive function fixed points
recursive function convergence
Language English
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Snippet A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions {fn} is...
A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions {fn } is...
A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions { f n } is...
A theorem is presented which has applications in the numerical computation of fixed points of recursive functions. If a sequence of functions {f(n)} is...
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StartPage 560
SubjectTerms convergence of numerical methods
convergent function sequence
metric space
numerical computation
recursive function convergence
recursive function fixed points
recursive functions
set theory
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Title Convergence of recursive functions on computers
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