Convergence of recursive functions on computers - Nepomuceno, Erivelton Geraldo (Journal of engineering (Stevenage, England), 2014)
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.