Local lagrange interpolation with cubic image splines on tetrahedral partitions Original Research Article

We describe an algorithm for constructing a Lagrange interpolation pair based on image cubic splines defined on tetrahedral partitions. In particular, given a set of points image, we construct a set P containing image and a spline space image based on a tetrahedral partition image whose set of vertices include image such that interpolation at the points of P is well-defined and unique. Earlier results are extended in two ways: (1) here we allow arbitrary sets image, and (2) the method provides optimal approximation order of smooth functions.