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A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones

Author

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  • R. H. AL-Obaidi
  • M. T. Darvishi
  • Predrag S. Stanimirović

Abstract

In order to compare different solvers for systems of nonlinear equations, some novel goodness and qualification criteria are defined in this paper. These use all parameters of a nonlinear solver such as convergence order, number of function evaluations, number of iterations, CPU time, etc. To achieve the criteria, different algorithms to solve nonlinear systems are categorised to three kinds. For any category, two criteria are defined to compare different algorithms in that category. As numerical results show, these new criteria can use to compare different algorithms which solve systems of nonlinear equations. Further, we present some corrected formulas for some classical efficiency indices and change them to be more applicable. Also, some suggestions are presented about the future works.

Suggested Citation

  • R. H. AL-Obaidi & M. T. Darvishi & Predrag S. Stanimirović, 2022. "A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones," Journal of Mathematics, Hindawi, vol. 2022, pages 1-20, September.
    • Handle: RePEc:hin:jjmath:4327913
    DOI: 10.1155/2022/4327913
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    Cited by:

    1. Chein-Shan Liu & Essam R. El-Zahar & Chih-Wen Chang, 2024. "Optimal Combination of the Splitting–Linearizing Method to SSOR and SAOR for Solving the System of Nonlinear Equations," Mathematics, MDPI, vol. 12(12), pages 1-24, June.
    2. Chein-Shan Liu & Chung-Lun Kuo & Chih-Wen Chang, 2024. "Matrix Pencil Optimal Iterative Algorithms and Restarted Versions for Linear Matrix Equation and Pseudoinverse," Mathematics, MDPI, vol. 12(11), pages 1-31, June.

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