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

Authors

  • 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

Keywords:

splines, first-degree splines, broken lines, splines with free knots, least-squares approximation, best approximation, minimal bactericidal concentration (MBC), minimal inhibitory concentration (MIC)

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

B¨ar, W., B¨ade-Schumann, U., Krebs, A., Cromme, L. J.: Rapid method for detection of minimal bactericidal concentration of antibiotics. Journal of Microbiological Methods, 77, 85-89, (2009)

Cromme, L. J.: Manifolds with cusps. Mathem. Nachrichten, 142, 219-234 (1989)

Cromme, L. J.: A unified approach to differential characterizations of local best approximations for exponential sums und splines. J. of Approximation Theory, 36(4), 294-303 (1982)

Cromme, L. J., Kunath, J.: Discrete approximation by first-degree splines with free knots. Preprint at https://arxiv.org (2017).

de Boor, C.: A practical guide to splines, Springer, New York (1978)

Jupp, D. L. B.: Approximation to data by splines with free knots. SIAM J. Numer. Anal., 15(2), 328-343 (1978)

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Published

2018-05-31

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

Issue

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

Section

Articles

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

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