Minimal-norm solution for Fredholm integral equation of the first kind with degenerate kernel implemented in finite steps

This article focuses on the Fredholm integral equation of the first kind with degenerate kernel in a reproducing kernel Hilbert space(RKHS). By applying the H-Hk formulation, an analytical minimal-norm solution is derived. Additionally, a sequential design approach is employed utilizing Gaussian process regression, which provides a fairly accurate approximation with the same quantity of observation points. Lastly, the viability of the proposed method is demonstrated through some illustrative examples.