On Shamanskii-Like Iterative Method for Solving Fuzzy Nonlinear Equations

 
 
 
  • Abstract
  • Keywords
  • References
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  • Abstract


    This paper proposes a Shamanskii-like method with fixed Jacobian matrix for solving fuzzy nonlinear equation. The method does not require evaluation of the Jacobian at every iteration. This is made possible by considering a fixed Jacobian at 15xn."> . Numerical experimentation are carried out, which shows the superiority of the proposed method against other existing methods.

     

     

     

  • Keywords


    Fuzzy nonlinear equations; parametric form; Fixed Jacobian; Shamanskii method.

  • References


      [1] Kelley, C. T. (1995). Iterative methods for linear and nonlinear equations. Frontiers in Applied Mathematics, 16, 575-601.

      [2] Sulaiman, I. M., Mamat, M., & Waziri, M. Y. (2018). Shamanskii method for solving fuzzy nonlinear equation. Proceedings of the 2nd IEEE International Conference on Intelligent Systems Engineering, pp. 1-4.

      [3] Zadeh, L. A. (1965). Information and control. Fuzzy Sets, 8(3), 338-353.

      [4] Abbasbandy, S., & Asady, B. (2004). Newton's method for solving fuzzy nonlinear equations. Applied Mathematics and Computation, 159(2), 349-356.

      [5] Buckley, J. J., & Qu, Y. (1990). Solving linear and quadratic fuzzy equations. Fuzzy Sets and Systems, 38(1), 43-59.

      [6] Broyden, C. G. (1965). A class of methods for solving nonlinear simultaneous equations. Mathematics of Computation, 19(92), 577-593.

      [7] Ramli, A., Abdullah, M. L., & Mamat, M. (2010). Broyden's method for solving fuzzy nonlinear equations. Advances in Fuzzy Systems, 2010, 1-6.

      [8] Fang, J. X. (2002). On nonlinear equations for fuzzy mappings in probabilistic normed spaces. Fuzzy Sets and Systems, 131(3), 357-364.

      [9] Peeva, K. (1992). Fuzzy linear systems. Fuzzy Sets and Systems, 49(3), 339-355.

      [10] Waziri, M. Y., & Moyi, A. U. (2016). An alternative approach for solving dual fuzzy nonlinear equations. International Journal of Fuzzy Systems, 18(1), 103-107.

      [11] Sulaiman, I. M., Mamat, M., Mohamed, M. A., & Waziri, M. Y. (2018). Diagonal updating Shamanskii-like method for solving fuzzy nonlinear equation. Far East Journal of Mathematical Sciences, 103(10), 1619-1629.

      [12] Sulaiman, I. M., Mamat, M., Waziri, M. Y., Fadhilah, A., & Kamfa. K. U. (2016). Regula Falsi method for solving fuzzy nonlinear equation. Far East Journal of Mathematical Sciences, 100(6), 873-884.

      [13] Sulaiman, I. M., Mamat, M., Waziri, M. Y., Mohamed, M. A., & Mohamad, F. S. (2018). Solving fuzzy nonlinear equation via Levenberg-Marquardt method. Far East Journal of Mathematical Sciences, 103(10), 1547-1558.

      [14] Sulaiman, I. M., Waziri, M. Y., Olowo, E. S., & Talat, A. N. (2018). Solving fuzzy nonlinear equations with a new class of conjugate gradient method. Malaysian Journal of Computing and Applied Mathematics, 1(1), 11-19.


 

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Article ID: 27381
 
DOI: 10.14419/ijet.v7i3.28.27381




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