Generalization of the Spline Interpolation Based on the Principle of the Compact Schemes

In this work the authors extend the high order compact difference schemes to the matching technique to develop a Local Matched Reconstruction theory that can be also considered as a generalization of the spline theory. The problem of the high order reconstructions correlated to an optimal matching in overlapping regions for contiguous expansions in one or more dimensions is stressed; some new generalized matched interpolations and their related numerical schemes are presented together with Fourier analysis of errors. Finally, some relevant aspects of the computational efforts associated to the various approaches are discussed.