@inproceedings{10d567b7fb704c82b154817a8ff6127a,
title = "Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data",
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).",
keywords = "Interpolation, Knots selection, Optimization, Reduced sparse data, Symbolic computation",
author = "Ryszard Kozera and Lyle Noakes",
year = "2017",
doi = "10.1007/978-3-319-66320-3_19",
language = "English",
isbn = "9783319663197",
volume = "10490 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer",
pages = "257--271",
editor = "Gerdt, {Vladimir P. } and Koepf, {Wolfram } and Seiler, {Werner M. } and Vorozhtsov, {Evgenii V. }",
booktitle = "Computer Algebra in Scientific Computing",
address = "Netherlands",
note = "19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017 ; Conference date: 18-09-2017 Through 22-09-2017",
}