An iterative stochastic procedure with a general step to a linear regular inverse problem

Abstract

In this paper we consider a linear operator equation in a Hilbert space. Using Hoeffding inequalities, an exponential bound to the solution obtained by a stochastic procedure is established and the values of the step ak for which the procedure converges almost completely (a.co) are discussed. An illustrative application was treated to the solution of a Fredholm integral equation of the second kind.