The problem of solving numerically a Fredholm integral equation of the first kind when it is known that f(x)>or=0, by a regularization method based on minimization is considered. The convergence of solutions of this minimization problem, given conditions on the data and the regularization parameter lambda , is demonstrated to show that the procedure leads to a correct regularization method. A generalized cross validation strategy for the selection of the regularization parameter is introduced. A number of numerical experiments are made and comparisons are made with Tikhonov regularization schemes based on differential operators.

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