Abstract
The problem of fitting multidimensional reduced data \(\mathcal{M}_n\) is discussed here. The unknown interpolation knots \(\mathcal{T}\) are replaced by optimal knots which minimize a highly non-linear multivariable function \(\mathcal{J}_0\). The numerical scheme called Leap-Frog Algorithm is used to compute such optimal knots for \(\mathcal{J}_0\)via the iterative procedure based in each step on single variable optimization of \(\mathcal{J}_0^{(k,i)}\). The discussion on conditions enforcing unimodality of each \(\mathcal{J}_0^{(k,i)}\) is also supplemented by illustrative examples both referring to the generic case of Leap-Frog. The latter forms a new insight on fitting reduced data and modelling interpolants of \(\mathcal{M}_n\).
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Kozera, R., Noakes, L., Wiliński, A. (2021). Generic Case of Leap-Frog Algorithm for Optimal Knots Selection in Fitting Reduced Data. In: Paszynski, M., Kranzlmüller, D., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M. (eds) Computational Science – ICCS 2021. ICCS 2021. Lecture Notes in Computer Science(), vol 12745. Springer, Cham. https://doi.org/10.1007/978-3-030-77970-2_26
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