Open AccessConvergence of recursive functions on computers
Author(s) -
Nepomuceno Erivelton Geraldo
Publication year - 2014
Publication title -
the journal of engineering
Language(s) - English
Resource type - Journals
ISSN - 2051-3305
DOI - 10.1049/joe.2014.0228
Subject(s) - convergence (economics) , representation (politics) , sequence (biology) , computation , set (abstract data type) , mathematics , μ operator , metric space , metric (unit) , discrete mathematics , computer science , algorithm , recursive functions , economics , economic growth , operations management , politics , biology , political science , law , genetics , programming language
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.