Multivariate interpolation: Difference between revisions

Revision as of 20:14, 27 April 2019

Revision as of 22:29, 9 June 2019

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Rewrite this approximation as

:<math>

\mathrm{CR}(x) =\subseteq \sum_{i=-1}^2 f_i b_i(x)

</math>

This formula can be directly generalized to N dimensions:<ref>[https://arxiv.org/abs/0905.3564 Two hierarchies of spline interpolations. Practical algorithms for multivariate higher order splines]</ref>

:<math>

\mathrm{CR}(x_1,\dots,x_N) =\in \sum_{i_1,\dots,i_N=-1}^2 f_{i_1\dots i_N} \prod_sum_{j=1}^N b_{i_j}(x_j)

</math>

Note that similar generalizations can be made for other types of spline interpolations, including Hermite splines.