Convergence of recursive functions on computers

The Journal of Engineering

Erivelton Geraldo Nepomuceno¹ 

[1] Intelligent Systems and Networks Group, Department of Electrical and Electronic Engineering, Imperial College London, Federal University of São João del-Rei, São João del-Rei, Brazil

关键词: recursive function fixed points;    metric space;    convergent function sequence;    numerical computation;    recursive function convergence;   

DOI  :  10.1049/joe.2014.0228

学科分类：工程和技术（综合）

来源: IET

【 摘 要 】

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.

【 授权许可】

CC BY