International Journal For Research In Mathematics And Statistics

Vol. 4 No. 5 (2018): International Journal For Research In Mathematics And Statistics
Articles

Discrete Approximation by First-Degree Splines with Free Knots

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  • Jens Kunath,
  • Ludwig J. Cromme
Jens Kunath
Numerische und Angewandte Mathematik, BTU Cottbus-Senftenberg, Platz der Deutschen Einheit 1, D-03046 Cottbus, Germany
Ludwig J. Cromme
Numerische und Angewandte Mathematik, BTU Cottbus-Senftenberg, Platz der Deutschen Einheit 1, D-03046 Cottbus, Germany
DOI: https://doi.org/10.53555/ms.v4i5.621

Published 2018-05-31

Keywords

  • splines of degree one,
  • splines with free knots,
  • best approximation,
  • discrete approx- imation,
  • Lp-approximation (1 ≤ p ≤ ∞),
  • existence theorem,
  • first-degree splines,
  • broken lines
    • ...More
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How to Cite

Kunath, J., & Cromme, L. J. (2018). Discrete Approximation by First-Degree Splines with Free Knots. International Journal For Research In Mathematics And Statistics, 4(5), 26–39. https://doi.org/10.53555/ms.v4i5.621

Copyright (c) 2018 International Journal For Research In Mathematics And Statistics (ISSN: 2208-2662)

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Abstract

This paper deals with the approximation of discrete real-valued functions by first-degree splines (broken lines) with free knots for arbitrary Lp-norms (1 ≤ p ≤ ∞). We prove the existence of best approximations und derive statements on the position of the (free) knots of a best approximation. Building on this, elsewhere we develop an algorithm to determine a (global) best approximation in the L2-norm.

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References

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