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Structured diagonal Gauss–Newton method for nonlinear least squares

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Abstract

This work proposes a structured diagonal Gauss–Newton algorithm for solving zero residue nonlinear least-squares problems. The matrix corresponding to the Gauss–Newton direction is approximated with a diagonal matrix that satisfies the structured secant condition. Using a derivative-free Armijo-type line search with some appropriate conditions, we prove that the proposed algorithm converges globally. Furthermore, the algorithm achieved R-linear convergence rate for zero residue problems. Numerical result shows that the algorithm is competitive with the existing algorithms in the literature.

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Acknowledgements

The authors are grateful to the referees for their constructive suggestions which improved the quality of the earlier version of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, School of Science and Technology, Federal Polytechnic, Kaura-Namoda, Zamfara, Nigeria

    Kamaluddeen Umar Danmalam

  2. Numerical Optimization Research Group, Bayero University, Kano, Nigeria

    Kamaluddeen Umar Danmalam, Hassan Mohammad & Mohammed Yusuf Waziri

  3. Department of Mathematical Sciences, Faculty of Physical Sciences, Bayero University, 700241, Kano, Nigeria

    Hassan Mohammad & Mohammed Yusuf Waziri

Authors
  1. Kamaluddeen Umar Danmalam
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  2. Hassan Mohammad
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  3. Mohammed Yusuf Waziri
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Correspondence to Hassan Mohammad.

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Communicated by Orizon Pereira Ferreira.

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Danmalam, K.U., Mohammad, H. & Waziri, M.Y. Structured diagonal Gauss–Newton method for nonlinear least squares. Comp. Appl. Math. 41, 68 (2022). https://doi.org/10.1007/s40314-022-01774-w

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  • DOI: https://doi.org/10.1007/s40314-022-01774-w

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