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Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data

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Computer Algebra in Scientific Computing (CASC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10490))

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Abstract

The problem of fitting sparse reduced data in arbitrary Euclidean space is discussed in this work. In our setting, the unknown interpolation knots are determined upon solving the corresponding optimization task. This paper outlines the non-linearity and non-convexity of the resulting optimization problem and illustrates the latter in examples. Symbolic computation within Mathematica software is used to generate the relevant optimization scheme for estimating the missing interpolation knots. Experiments confirm the theoretical input of this work and enable numerical comparisons (again with the aid of Mathematica) between various schemes used in the optimization step. Modelling and/or fitting reduced sparse data constitutes a common problem in natural sciences (e.g. biology) and engineering (e.g. computer graphics).

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Kozera, R., Noakes, L. (2017). Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2017. Lecture Notes in Computer Science(), vol 10490. Springer, Cham. https://doi.org/10.1007/978-3-319-66320-3_19

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  • DOI: https://doi.org/10.1007/978-3-319-66320-3_19

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