A least square point of view to reproducing kernel methods to solve functional equations

摘要

In this paper we discuss and present a least square and a QR point of view to reproducing kernel methods to approximate solutions to some linear and nonlinear functional equations. The procedure we discuss here may includes ordinary, partial differential, and integral equations. We also give new proofs to some known results on this subject. The most interesting contribution is that the proposed algorithm may work even when we know a reproducing kernel but nothing more about the associated reproducing kernel Hilbert space, including the inner product structure.