This paper is concerned with the ubiquitous inverse problem of recovering an unknown function u from finitely many measurements, possibly affected by noise. In recent years, inversion methods based on linear approximation spaces were introduced in [1, 2] certified recovery bounds. It however known that become ineffective for approximating simple and relevant families functions, such as piecewis...

Abstract A variational principle is established by the semi-inverse method and used to solve approximately a nonlinear problem Ritz method. In this process,it may be difficult large system of algebraic equations,the Groebner bases theory (Buchberger’s algorithm) applied problem. The results show that approach much simpler more efficient.