Exponential inequalities for Mann's stochastic algorithm. Issue 1 (2nd January 2020) - Allouti, Chahira; Barache, Bahia; Dahmani, Abdelnasser
Abstract: In this article, we investigate the problem of approximating the fixed point for some function using a Mann iterative process with random errors. After establishing some exponential inequalities, we prove the complete convergence of Mann's algorithm toward the fixed point and deduce a confidence interval for this one. In addition, we establish the convergence rate of Mann's algorithm. Several numerical examples are sketched to illustrate the performance of the proposed algorithm.