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

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  • R. H. AL-Obaidi
  • M. T. Darvishi

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, 2022. "A Comparative Study on Qualification Criteria of Nonlinear Solvers with Introducing Some New Ones," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:4327913
    DOI: 10.1155/2022/4327913
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    References listed on IDEAS

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    1. Fayyaz Ahmad & Shafiq Ur Rehman & Malik Zaka Ullah & Hani Moaiteq Aljahdali & Shahid Ahmad & Ali Saleh Alshomrani & Juan A. Carrasco & Shamshad Ahmad & Sivanandam Sivasankaran, 2017. "Frozen Jacobian Multistep Iterative Method for Solving Nonlinear IVPs and BVPs," Complexity, Hindawi, vol. 2017, pages 1-30, May.
    2. Alicia Cordero & Cristina Jordán & Esther Sanabria & Juan R. Torregrosa, 2019. "A New Class of Iterative Processes for Solving Nonlinear Systems by Using One Divided Differences Operator," Mathematics, MDPI, vol. 7(9), pages 1-12, August.
    3. Cordero, Alicia & Gutiérrez, José M. & Magreñán, Á. Alberto & Torregrosa, Juan R., 2016. "Stability analysis of a parametric family of iterative methods for solving nonlinear models," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 26-40.
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    Cited by:

    1. Xin Li & Wei Ma, 2025. "A Fourth‐Order Ulm‐Type Method for Inverse Eigenvalue Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2025(1).

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