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2021 | OriginalPaper | Chapter

Generic Case of Leap-Frog Algorithm for Optimal Knots Selection in Fitting Reduced Data

Authors : Ryszard Kozera, Lyle Noakes, Artur Wiliński

Published in: Computational Science – ICCS 2021

Publisher: Springer International Publishing

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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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Title: Generic Case of Leap-Frog Algorithm for Optimal Knots Selection in Fitting Reduced Data
Authors: Ryszard Kozera
Lyle Noakes
Artur Wiliński
Publisher: Springer International Publishing
Book: Computational Science – ICCS 2021
Print ISBN: 978-3-030-77969-6

Electronic ISBN: 978-3-030-77970-2

Copyright Year: 2021
DOI: https://doi.org/10.1007/978-3-030-77970-2_26

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