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Scattered multidimensional interpolation is one of the most important - and hard to solve - practical problems.Another important problem is scattered fitting with smoothing, which differs from interpolation by presence of noisein the data and need for controlled smoothing.
Very often you just can't sample function at regular grid.For example, when you sample geospatial data,you can't allocate measurement points as you wish - some places at this planet are hard to reach.However, you may have many irregularly located points with known function values.Such irregular grid may have structure, points may follow some pattern - but it is not rectangular,and it makes impossible to apply two classic interpolation methods (2D/3D splines and polynomials).
ALGLIB package offers you two versions of improved RBF algorithm.ALGLIB implementation of RBF's uses compact (Gaussian) basis functions and many tricks to improve speed,convergence an
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