Multidimensional spline integration of scattered data

Details Multidimensional spline integration of scattered data Multidimensional spline integration of scattered data

2010-10-14

arxiv.org/abs/1010.2952v2

Physics

Computational Physics

12 pages, 7 figures

Scientific paper

We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing the deviation between its derivatives and the measured gradient. Unlike a multidimensional integration along some path, the present method results in a continuous, smooth surface, furthermore, it also applies to input data that are non-equidistant and not aligned on a rectangular grid. Function values, first and second derivatives and integrals are easy to calculate. The proper estimation of the statistical and systematical errors is also incorporated in the method.

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