Kriging and splines with derivative information

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Abstract
Spline fitting is a popular method of interpolating a real-valued function given its values at a set of points in Rd. Other linear constraints such as derivative information can also be incorporated as we show here. Spline fitting is well known to be a special case of kriging. Using the kriging framework we give a full description of the theory including algorithms for computation, and various special cases are discussed. An application is given to the construction of deformations with landmark, tangent and curvature constraints.

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