Regularized minimal-norm solution of an overdetermined system of first kind integral equations

Overdetermined systems of first kind integral equations appear in many applications. When the right-hand side is discretized, resulting finite-data problem ill-posed and admits infinitely solutions. We propose a numerical method to compute minimal-norm solution presence boundary constraints. The algorithm stems from Riesz representation theorem operates reproducing kernel Hilbert space. Since linear system strongly ill-conditioned, we construct regularization depending on discrete parameter. It based expansion terms singular functions operator defining problem. Two estimation techniques are tested for automatic determination parameter, namely, discrepancy principle L-curve method. Numerical results concerning two artificial test problems demonstrate excellent performance proposed Finally, particular model typical geophysical applications, which reproduces readings frequency domain electromagnetic induction device, investigated. show that new extremely effective when sought smooth, but produces significant information even non-smooth