Projection methods for the solution of Fredholm integral equations of the first kind with $(ϕ, β)$-differentiable kernels and random errors

Abstract

We estimate errors of projection methods for the solution of the Fredholm equaitons of the first kindAx=y+ζ with random perturbation ζ under the assumption that the integral operatorA has a (ϕ, β)-differentiable kernel and the mathematical expectation of ∥ξ∥² does not exceed σ². Under these assumptions, we obtain an estimate that is a complete analog of the well-known result by Vainikko and Plato for the deterministic case where ∥ξ∥≤σ.