论文信息 - A family of new Newton-like methods

A family of new Newton-like methods

Abstract In this paper, we present a family of new Newton-like methods, which removes the severe condition f ′ ( x ) ≠ 0 in a neighborhood of the required root imposed on Newton’s method. The new methods are quadratically convergent and moreover, have the same error equation as Newton’s method. The detailed analysis of convergence is supplied. The numerical results show that the new methods have definite practical utility.

Yitian Li | Jisheng Kou

[1] Xinyuan Wu,et al. A new continuation Newton-like method and its deformation , 2000, Appl. Math. Comput..

[2] Yitian Li,et al. Efficient continuation Newton-like method for solving systems of non-linear equations , 2006, Appl. Math. Comput..

[3] James M. Ortega,et al. Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[4] J. Stoer,et al. Introduction to Numerical Analysis , 2002 .

[5] Xinyuan Wu. Newton-like method with some remarks , 2007, Appl. Math. Comput..