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

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

2009-11-16

arxiv.org/abs/0911.3071v2

Mathematics

Numerical Analysis

29 pages

Scientific paper

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 $T:=K^*K,\quad T_a:=T+aI,\quad q\in(0,1),\quad a_n:=\alpha_0q^n, \alpha_0>0,$ with finite-dimensional approximations of $T$ and $K^*$ for solving stably Fredholm integral equations of the first kind with noisy data.

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