论文信息 - Modified Jarratt method with sixth-order convergence

Modified Jarratt method with sixth-order convergence

In this paper, we present a variant of Jarratt method with order of convergence six for solving non-linear equations. Per iteration the method requires two evaluations of the function and two of its first derivatives. The new multistep iteration scheme, based on the new method, is developed and numerical tests verifying the theory are also given.

Yitian Li | Xiuhua Wang | Jisheng Kou

[1] Miquel Grau. An Improvement to the Computing of Nonlinear Equation Solutions , 2004, Numerical Algorithms.

[2] A. Householder. Solution of Equations and Systems of Equations (A. M. Ostrowski) , 1967 .

[3] Changbum Chun,et al. Some improvements of Jarratt's method with sixth-order convergence , 2007, Appl. Math. Comput..

[4] Yitian Li,et al. A family of fifth-order iterations composed of Newton and third-order methods , 2007, Appl. Math. Comput..

[5] José Luis Díaz-Barrero,et al. An improvement of the Euler-Chebyshev iterative method , 2006 .

[6] Yitian Li,et al. An improvement of the Jarratt method , 2007, Appl. Math. Comput..

[7] José Luis Díaz-Barrero,et al. An improvement to Ostrowski root-finding method , 2006, Appl. Math. Comput..

[8] Ioannis K. Argyros,et al. The Jarratt method in Banach space setting , 1994 .

[9] Miquel Grau-Sánchez,et al. A variant of Cauchy's method with accelerated fifth-order convergence , 2004, Appl. Math. Lett..