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New Mono‐ and Biaccelerator Iterative Methods with Memory for Nonlinear Equations

Author

Listed:
  • T. Lotfi
  • F. Soleymani
  • S. Shateyi
  • P. Assari
  • F. Khaksar Haghani

Abstract

Acceleration of convergence is discussed for some families of iterative methods in order to solve scalar nonlinear equations. In fact, we construct mono‐ and biparametric methods with memory and study their orders. It is shown that the convergence orders 12 and 14 can be attained using only 4 functional evaluations, which provides high computational efficiency indices. Some illustrations will also be given to reverify the theoretical discussions.

Suggested Citation

  • T. Lotfi & F. Soleymani & S. Shateyi & P. Assari & F. Khaksar Haghani, 2014. "New Mono‐ and Biaccelerator Iterative Methods with Memory for Nonlinear Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:705674
    DOI: 10.1155/2014/705674
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    References listed on IDEAS

    as
    1. F. Soleymani & M. Sharifi & S. Shateyi, 2014. "Approximating the Inverse of a Square Matrix with Application in Computation of the Moore-Penrose Inverse," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, March.
    2. F. Soleymani & M. Sharifi & S. Shateyi, 2014. "Approximating the Inverse of a Square Matrix with Application in Computation of the Moore‐Penrose Inverse," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. T. Lotfi & F. Soleymani & S. Sharifi & S. Shateyi & F. Khaksar Haghani, 2014. "Multipoint Iterative Methods for Finding All the Simple Zeros in an Interval," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-13, July.
    4. F. Soleymani & D. K. R. Babajee & S. Shateyi & S. S. Motsa, 2012. "Construction of Optimal Derivative‐Free Techniques without Memory," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    5. F. Soleymani & D. K. R. Babajee & S. Shateyi & S. S. Motsa, 2012. "Construction of Optimal Derivative-Free Techniques without Memory," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-24, November.
    6. F. Soleymani & E. Tohidi & S. Shateyi & F. Khaksar Haghani, 2014. "Some Matrix Iterations for Computing Matrix Sign Function," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, July.
    7. T. Lotfi & F. Soleymani & S. Sharifi & S. Shateyi & F. Khaksar Haghani, 2014. "Multipoint Iterative Methods for Finding All the Simple Zeros in an Interval," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    8. F. Soleymani & E. Tohidi & S. Shateyi & F. Khaksar Haghani, 2014. "Some Matrix Iterations for Computing Matrix Sign Function," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    Full references (including those not matched with items on IDEAS)

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