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Advances in Stochastic and Deterministic Global Optimization pp 209–226Cite as

On the Least-Squares Fitting of Data by Sinusoids

Part of the Springer Optimization and Its Applications book series (SOIA,volume 107)

Abstract

The sinusoidal parameter estimation problem is considered to fit a sum of damped sinusoids to a series of noisy observations. It is formulated as a nonlinear least-squares global optimization problem. A one-parametric case study is examined to determine an unknown frequency of a signal. Univariate Lipschitz-based deterministic methods are used for solving such problems within a limited computational budget. It is shown that the usage of local information in these methods (such as local tuning on the objective function behavior and/or evaluating the function first derivatives) can significantly accelerate the search for the problem solution with a required guarantee. Results of a numerical comparison with metaheuristic techniques frequently used in engineering design are also reported and commented on.

Keywords

  • Nonlinear regression
  • Least-squares fitting
  • Lipschitz-based deterministic methods
  • Metaheuristics
  • Numerical comparison

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Acknowledgements

This work was supported by the Russian Science Foundation, project number 15-11-30022 “Global optimization, supercomputing computations, and applications.”

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Authors and Affiliations

  1. Dipartimento di Ingegneria Informatica, Modellistica, Elettronica e Sistemistica, Università della Calabria, Via P. Bucci, Cubo, 42C – 87036, Rende, (CS), Italy

    Yaroslav D. Sergeyev, Dmitri E. Kvasov & Marat S. Mukhametzhanov

  2. Department of Software and Supercomputing Technologies, Lobachevsky State University of Nizhni Novgorod, Nizhny Novgorod, Russia

    Yaroslav D. Sergeyev, Dmitri E. Kvasov & Marat S. Mukhametzhanov

Authors
  1. Yaroslav D. Sergeyev
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  2. Dmitri E. Kvasov
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  3. Marat S. Mukhametzhanov
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Corresponding author

Correspondence to Yaroslav D. Sergeyev .

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Editors and Affiliations

  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida, USA

    Panos M. Pardalos

  2. Cardiff School of Mathematics, Cardiff University, Cardiff, United Kingdom

    Anatoly Zhigljavsky

  3. Institute of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania

    Julius Žilinskas

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Sergeyev, Y.D., Kvasov, D.E., Mukhametzhanov, M.S. (2016). On the Least-Squares Fitting of Data by Sinusoids. In: Pardalos, P., Zhigljavsky, A., Žilinskas, J. (eds) Advances in Stochastic and Deterministic Global Optimization. Springer Optimization and Its Applications, vol 107. Springer, Cham. https://doi.org/10.1007/978-3-319-29975-4_11

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