title: A new Newton-like method for solving nonlinear equations.
abstract: This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.
authors.affiliation: College of Mathematics Science, Inner Mongolia University, Hohhot, 010021 China ; College of Mathematical Science, Inner Mongolia Normal University, Hohhot, 010022 China.
authors.forename: B
authors.identifier: 0000-0002-0398-1452
authors.initials: B
authors.lastname: Saheya
authors.affiliation: College of Mathematics Science, Inner Mongolia University, Hohhot, 010021 China.
authors.forename: Guo-Qing
authors.initials: GQ
authors.lastname: Chen
authors.affiliation: College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing, 100124 China.
authors.forename: Yun-Kang
authors.initials: YK
authors.lastname: Sui
authors.affiliation: College of Mathematics Science, Inner Mongolia University, Hohhot, 010021 China.
authors.forename: Cai-Ying
authors.initials: CY
authors.lastname: Wu
keywords: Improved Newton’s method; Local convergence; Rational approximate function