Interpolation of scattered data in R^3 using minimum L_p-norm networks, 1<p<∞
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We consider the extremal problem of interpolation of scattered data in R^3 by smooth curve networks with minimal L_p-norm of the second derivative for 1<p<∞. The problem for p=2 was set and solved by Nielson (1983). Andersson et al. (1995) gave a new proof of Nielson's result by using a different approach. Partial results for the problem for 1<p<∞ were announced without proof in (Vlachkova (1992)). Here we present a complete characterization of the solution for 1<p<∞. Numerical experiments are visualized and presented to illustrate and support our results.
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