Vlachkova, Krassimira2024-07-122024-07-122019Vlachkova, K. (2019). Interpolation of scattered data in R 3 using minimum lp-norm networks, 1 < p < ?. International Conference of Mathematical Sciences (ICMS 2019). s. 135.978-605-2124-29-1https://hdl.handle.net/20.500.12415/2134We consider the extremal problem of interpolation of scattered data in R 3 by smooth curve networks with minimal Lp-norm of the second derivative for 1 < p < ?. The problem for p = 2 was set and solved by Nielson [1]. Andersson et al. [2] gave a new proof of Nielson’s result by using a different approach. It allowed them to set and solve the constrained extremal problem of interpolation of convex scattered data in R 3 by minimum L2-norm networks that are convex along the edges of an associated triangulation. Partial results for the unconstrained and the constrained problems were announced without proof in [3]. Here we present complete characterization of the solutions to both the unconstrained and the constrained problems for 1 < p < ?.enCC0 1.0 Universalinfo:eu-repo/semantics/openAccessExtremal scattered data interpolationMinimum norm networksArticle136135