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<p>The investigation on the relationship between high-order iterations with and without derivatives for resolving systems of nonlinear equations is presented in this publication. We define sufficient convergence conditions for parameter matrices by defining the relationship between derivative-based and derivative-free approaches. We propose families of higher-order derivative-free methods and provide implementation algorithms for parameter matrices. The proposed methods can be useful for cases where analytical expressions for Jacobian matrices are difficult to obtain. The paper targets researchers and practitioners in the field of numerical analysis and computational mathematics.</p>

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ON THE CONNECTION BETWEEN HIGH-ORDER ITERATIONS WITH AND WITHOUT DERIVATIVES FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

  • 期刊论文

  • 发表日期：

    2025年8月11日

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  • Zhanlav Tugal,
  • Mijiddorj Renchin-Ochir

摘要

The investigation on the relationship between high-order iterations with and without derivatives for resolving systems of nonlinear equations is presented in this publication. We define sufficient convergence conditions for parameter matrices by defining the relationship between derivative-based and derivative-free approaches. We propose families of higher-order derivative-free methods and provide implementation algorithms for parameter matrices. The proposed methods can be useful for cases where analytical expressions for Jacobian matrices are difficult to obtain. The paper targets researchers and practitioners in the field of numerical analysis and computational mathematics.