The L-pseudo-solution using stochastic algorithm of Landweber

In this paper, we consider a linear equation Ax=u. A is an operator with an unbounded inverse in a Hilbert space. The right side u does not belong to the range of A. Obviously, a solution in classical sense does not exist and A ^?1 u does not have a sense. To solve this problem arising from many experimental fields of science, where the second member u stems from measurements, we propose a recurrent procedure which converges almost completely and in quadratic mean to L-pseudo-solution and for which we build up a confidence interval. To check the validity of our results, a numerical example which is standard in rheology is proposed.