2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57160I offer a simple and useful formula for the resolvent of a small rank perturbation of large matrices. I discuss applications of this formula, in particular, to analytical and numerical solving of difference boundary value problems. I present examples connected with such problems for the difference Laplacian and estimate numerical efficiency of the corresponding algorithms.arXiv version is already officialMathematical PhysicsAnalysis of PDEstext