International Journal For Research In Mathematics And Statistics

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

Computing Best Discrete Least-Squares Approximations by First-Degree Splines with Free Knots

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  • Ludwig J. Cromme,
  • Jens Kunath,
  • Andreas Krebs
Ludwig J. Cromme
Numerische und Angewandte Mathematik, BTU Cottbus-Senftenberg, Platz der Deutschen Einheit 1, D-03046 Cottbus, Germany
Jens Kunath
Numerische und Angewandte Mathematik, BTU Cottbus-Senftenberg, Platz der Deutschen Einheit 1, D-03046 Cottbus, Germany
Andreas Krebs
Aerodynamik und Stro¨mungslehre , BTU Cottbus-Senftenberg, Siemens-Halske-Ring 14, D-03046 Cottbus, Germany
DOI: https://doi.org/10.53555/ms.v4i5.620

Published 2018-05-31

Keywords

  • splines,
  • first-degree splines,
  • broken lines,
  • splines with free knots,
  • least-squares approximation,
  • best approximation,
  • minimal bactericidal concentration (MBC),
  • minimal inhibitory concentration (MIC)
    • ...More
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How to Cite

Cromme, L. J., Kunath, J., & Krebs, A. (2018). Computing Best Discrete Least-Squares Approximations by First-Degree Splines with Free Knots. International Journal For Research In Mathematics And Statistics, 4(5), 11–25. https://doi.org/10.53555/ms.v4i5.620

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

We present an algorithm to compute best least-squares approximations of discrete real-valued functions by first-degree splines (broken lines) with free knots. We demonstrate that the algorithm delivers after a finite number of steps a (global) best approximation. The analysis is complemented by remarks on programming and by a number of numerical examples including applications from medicine (MBC, MIC). Key words: splines, first-degree splines, broken lines, splines with free knots, least-squares approximation, best approximation, minimal bactericidal concentration (MBC), minimal inhibitory concentration (MIC).

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References

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