Abstract
In this paper, we present a new sixth-order iterative method for solving nonlinear systems and prove a local convergence result. The new method requires solving five linear systems per iteration. An important feature of the new method is that the LU (lower upper, also called LU factorization) decomposition of the Jacobian matrix is computed only once in each iteration. The computational efficiency index of the new method is compared to that of some known methods. Numerical results are given to show that the convergence behavior of the new method is similar to the existing methods. The new method can be applied to small- and medium-sized nonlinear systems.
Highlights
We consider the problem of finding a zero of a nonlinear function F : D ⊂ Rm → Rm, that is, a solution α of the nonlinear system F ( x ) = 0 with m equations and m unknowns
We have proposed a new iterative method of order six for solving nonlinear systems
Five linear systems are required to be solved in each iteration, the LU decomposition of the linear systems are computed only once per full iteration
Summary
In order to accelerate the convergence or to reduce the computational cost and function evaluation in each step of the iterative process, many efficient methods have been proposed for solving nonlinear. Method (3) is denoted by CM4 and requires LU decomposition of the Jacobian matrix only once per full iteration. The purpose of this paper is to construct a new sixth-order iterative method for solving small- and medium-sized systems. The theoretical advantages of the new method are based on the assumption that the Jacobian matrix is dense and that LU factorization is used to solve systems with the Jacobian.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
