An Algorithm for Computing Minimum Norm Solutions of Fredholm Integral Equations of the First Kind

An algorithm is developed for the numerical computation of minimum norm solutions of Fredholm integral equations of the first kind $Kf = g$. The algorithm is different from Tihonov’s method and avoids direct collocation. The method has the following geometrical interpretation: One is looking for a vector of minimum norm that lies in a given finite dimensional subspace and also in a given neighborhood of the set of all solutions of $Kf = g$. A convergence proof for the algorithm is presented and four examples are treated numerically.