An iterative method for solving Fredholm integral equations of the first kind
arXiv:0911.307111 citations
Originality Synthesis-oriented
AI Analysis
This work addresses the need for stable numerical solutions to ill-posed integral equations, which is important for inverse problems in science and engineering.
The paper provides a convergence analysis of an iterative scheme for stably solving Fredholm integral equations of the first kind with noisy data, using finite-dimensional approximations.
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 $T:=K^*K,\quad T_a:=T+aI,\quad q\in(0,1),\quad a_n:=α_0q^n, α_0>0,$ with finite-dimensional approximations of $T$ and $K^*$ for solving stably Fredholm integral equations of the first kind with noisy data.