### 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).

Original language | English |
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Title of host publication | Computer Algebra in Scientific Computing |

Subtitle of host publication | 19th International Workshop, CASC 2017, Proceedings |

Editors | Vladimir P. Gerdt, Wolfram Koepf, Werner M. Seiler, Evgenii V. Vorozhtsov |

Place of Publication | Beijing |

Publisher | Springer |

Pages | 257-271 |

Number of pages | 15 |

Volume | 10490 LNCS |

ISBN (Print) | 9783319663197 |

DOIs | |

Publication status | Published - 2017 |

Event | 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017 - Beijing, China Duration: 18 Sep 2017 → 22 Sep 2017 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 10490 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017 |
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Country | China |

City | Beijing |

Period | 18/09/17 → 22/09/17 |

### Fingerprint

### Cite this

*Computer Algebra in Scientific Computing: 19th International Workshop, CASC 2017, Proceedings*(Vol. 10490 LNCS, pp. 257-271). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10490 LNCS). Beijing: Springer. https://doi.org/10.1007/978-3-319-66320-3_19

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*Computer Algebra in Scientific Computing: 19th International Workshop, CASC 2017, Proceedings.*vol. 10490 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10490 LNCS, Springer, Beijing, pp. 257-271, 19th International Workshop on Computer Algebra in Scientific Computing, CASC 2017, Beijing, China, 18/09/17. https://doi.org/10.1007/978-3-319-66320-3_19

**Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data.** / Kozera, Ryszard; Noakes, Lyle.

Research output: Chapter in Book/Conference paper › Conference paper

TY - GEN

T1 - Non-linearity and Non-convexity in Optimal Knots Selection for Sparse Reduced Data

AU - Kozera, Ryszard

AU - Noakes, Lyle

PY - 2017

Y1 - 2017

N2 - 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).

AB - 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).

KW - Interpolation

KW - Knots selection

KW - Optimization

KW - Reduced sparse data

KW - Symbolic computation

UR - http://www.scopus.com/inward/record.url?scp=85029799641&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-66320-3_19

DO - 10.1007/978-3-319-66320-3_19

M3 - Conference paper

SN - 9783319663197

VL - 10490 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 257

EP - 271

BT - Computer Algebra in Scientific Computing

A2 - Gerdt, Vladimir P.

A2 - Koepf, Wolfram

A2 - Seiler, Werner M.

A2 - Vorozhtsov, Evgenii V.

PB - Springer

CY - Beijing

ER -