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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Vydané v:	Journal of engineering (Stevenage, England) Ročník 2014; číslo 10; s. 560 - 562
Hlavný autor:	Nepomuceno, Erivelton Geraldo
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	The Institution of Engineering and Technology 01.10.2014 Wiley
Predmet:	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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Popis
Shrnutí:	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.
ISSN:	2051-3305 2051-3305
DOI:	10.1049/joe.2014.0228