Iterative methods in ill-posed problems with random errors (Q1064018)

For an ill-posed linear equation \(A_ 0u=f_ 0\) in a Hilbert space an iterative scheme \(u_{n+1}=u_ n-A^*A u_ n+A^*f+w_ n\), \(n\geq 0\), is applied. Here \(A-A_ 0\) and \(f-f_ 0\) are errors, and the \(w_ n\) are random errors. Under some ''smallness'' assumptions for the expectations and variances of the \(| w_ k|\) six different stopping rules are analyzed and their types of convergence (in probabilistic sense) are discussed.