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Abdelnasser Dahmani

Publications and source records attributed to Abdelnasser Dahmani.

2 recordsLinked to original sources
arXiv2017

Strongly mixed random errors in Mann's iteration algorithm for a contractive real function

This work deals with the Mann's stochastic iteration algorithm under strong mixing random errors. We establish the Fuk-Nagaev's inequalities that enable us to prove the almost complete convergence with its corresponding rate of convergence. Moreover, these inequalities give us the possibility of constructing a confidence interval for the unique fixed point. Finally, to check the feasibility and validity of our theoretical results, we consider some numerical examples, namely a classical example from astronomy.

math.PR↗
arXiv2017

Exponential inequalities for Mann's iterative scheme with functional random errors

In this work, we deal with an iteration method for approximating a fixed point of a contraction mapping using the Mann's algorithm under functional random errors. We first show its almost complete convergence to the fixed point by mean of an exponential inequality and then we specify the induced rate of convergence. We finally build a confidence set for the fixed point.

math.PR↗