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Nepomuceno, Erivelton (2014) Convergence of recursive functions on computers. Journal of Engineering, 10. pp. 560-562. ISSN 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.
| Item Type: | Article |
|---|---|
| Keywords: | Convergence; recursive; functions; computers; |
| Academic Unit: | Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute |
| Item ID: | 16836 |
| Identification Number: | 10.1049/joe.2014.0228 |
| Depositing User: | Erivelton Nepomuceno |
| Date Deposited: | 10 Jan 2023 15:34 |
| Journal or Publication Title: | Journal of Engineering |
| Publisher: | IET |
| Refereed: | Yes |
| Related URLs: | |
| URI: | https://mural.maynoothuniversity.ie/id/eprint/16836 |
| Use Licence: | This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here |
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