An iterative method for solving Fredholm integral equations of the first kind

Abstract

The purpose of this paper is to give a convergence analysis of the iterative scheme: \bee u_n^\dl=qu_{n-1}^\dl+(1-q)T_{a_n}^{-1}K^*f_\dl,\quad u_0^\dl=0,\eee where $T:=K^{\ast }K,T_a:=T+aI,q\in (0,1),a_n:={\alpha }_0{q}^n,{\alpha }_0>0,$ with finite-dimensional approximations of $T$ and $K^{\ast }$ for solving stably Fredholm integral equations of the first kind with noisy data.

29 pages