论文信息 - A multi-parameter family of three-step eighth-order iterative methods locating a simple root

A multi-parameter family of three-step eighth-order iterative methods locating a simple root

A multi-parameter family of three-step eighth-order iterative methods free from second derivatives are proposed in this paper to find a simple root of nonlinear algebraic equations. Convergence analysis as well as numerical experiments confirms the eighth-order convergence and asymptotic error constants.

Young Hee Geum | Young Ik Kim | Y. Geum

[1] L. Hörmander,et al. An introduction to complex analysis in several variables , 1973 .

[2] P. Jarratt. Some fourth order multipoint iterative methods for solving equations , 1966 .

[3] Stephen Wolfram,et al. The Mathematica book (4th edition) , 1999 .

[4] Stephen Wolfram,et al. The Mathematica Book , 1996 .

[5] Xia Wang,et al. Two new families of sixth-order methods for solving non-linear equations , 2009, Appl. Math. Comput..

[6] J. Traub. Iterative Methods for the Solution of Equations , 1982 .

[7] N. Levenberg,et al. Function theory in several complex variables , 2001 .

[8] L. Ahlfors. Complex Analysis , 1979 .

[9] Xiuhua Wang,et al. Some variants of Ostrowski's method with seventh-order convergence , 2007 .

[10] R. F. King. A Family of Fourth Order Methods for Nonlinear Equations , 1973 .

[11] Yitian Li,et al. A variant of Jarratt method with sixth-order convergence , 2008, Appl. Math. Comput..

[12] Qingbiao Wu,et al. A new family of eighth-order iterative methods for solving nonlinear equations , 2009, Appl. Math. Comput..

[13] Qingbiao Wu,et al. New variants of Jarratt’s method with sixth-order convergence , 2009, Numerical Algorithms.

[14] Changbum Chun,et al. Some sixth-order variants of Ostrowski root-finding methods , 2007, Appl. Math. Comput..