Abstract
The problem of fitting multidimensional reduced data is analyzed here . The missing interpolation knots \(\mathcal{T}\) are substituted by \(\hat{\mathcal{T}}\) which minimize a non-linear multivariate function \(\mathcal{J}_0\). One of numerical schemes designed to compute such optimal knots relies on iterative scheme called Leap-Frog Algorithm. The latter is based on merging the respective generic and non-generic univariate overlapping optimizations of \(\mathcal{J}_0^{(k,i)}\). The discussion to follow establishes the sufficient conditions enforcing unimodality of the non-generic case of \(\mathcal{J}_0^{(k,i)}\) (for special data set-up and its perturbation). Illustrative example supplements the analysis in question. This work complements already existing analysis on generic case of Leap-Frog Algorithm.
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Notes
- 1.
This work is a part of Polish National Centre of Research and Development research project POIR.01.02.00-00-0160/20.
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Kozera, R., Noakes, L. (2022). Non-Generic Case of Leap-Frog for Optimal Knots Selection in Fitting Reduced Data. In: Groen, D., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2022. ICCS 2022. Lecture Notes in Computer Science, vol 13352. Springer, Cham. https://doi.org/10.1007/978-3-031-08757-8_29
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