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A QUADRATICALLY CONVERGENT ITERATIVE METHOD FOR NONLINEAR EQUATIONS

윤병인|Miodrag S. Petkovic
대한수학회 (The Korean Mathematical Society)|2011.05|대한수학회지 (Journal of the KMS)|제48권 제3호|pp. 487-497

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참고문헌

키워드

hybrid methoditerative methodnonlinear equationquadratic convergence
주제분류수학

초록

In this paper we propose a simple iterative method for nding a root of a nonlinear equation. It is shown that the new method, which does not require any derivatives, has a quadratic convergence order. In addition, one can nd that a hybrid method combined with the non-iterative method can further improve the convergence rate. To show the efficiency of the presented method we give some numerical examples.

Abstract

In this paper we propose a simple iterative method for nding a root of a nonlinear equation. It is shown that the new method, which does not require any derivatives, has a quadratic convergence order. In addition, one can nd that a hybrid method combined with the non-iterative method can further improve the convergence rate. To show the efficiency of the presented method we give some numerical examples.

참고문헌 (14)

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  6. V. Kanwar, "Simple geometric constructions of quadratically and cubically convergent iterative functions to solve nonlinear equations", Numer. Algorithm, 47(1), pp.95~107 (2008)
  7. M. A. Noor, "Two-step iterative methods for nonlinear equa- tions", Appl. Math. Comput, 181(2), pp.1068~1075 (2006)
  8. A. M. Ostrowski, "Solution of Equations and Systems of Equations, Second edition. Pure and Applied Mathematics, Vol. 9" (1966), Academic Press
  9. L. D. Petkovic, "A note on some recent methods for solving nonlinear equations", Appl. Math. Comput, 185(1), pp.368~374 (2007)
  10. 윤병인, "Sigmoid-like functions and root finding methods", APPLIED MATHEMATICS AND COMPUTATION, 204(2), pp.784~793
  11. R. G. Voigt, "Orders of convergence for iterative procedures", SIAM J. Numer. Anal, 8, pp.222~243 (1971)
  12. X. Y. Wu, "An improved regula falsi method with quadratic convergence of both diameter and point for enclosing simple zeros of nonlinear equations", Appl. Math. Comput, 144(2), pp.381~388 (2003)
  13. 윤병인, "A non-iterative method for solving non-linear equations", APPLIED MATHEMATICS AND COMPUTATION, 198(2), pp.691~699
  14. 윤병인, "Iterative methods based on the signum function approach for solving nonlinear equations", NUMERICAL ALGORITHMS, 52(4), pp.649~662

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