A new cubic convergent method for solving a system of nonlinear equations. Issue 10 (3rd October 2017)

• Record Type: Journal Article
• Authors: Yang, Weiwei; Ni, Qin
• Is Part Of: International journal of computer mathematics. Volume 94:Issue 10(2017)
• Page Start: 1968
• Page End: 1980
• Publication Date: 2017-10-03
• Subjects: Cubic convergence -- global convergence -- Chebyshev's method -- nonlinear equations -- nonmonotone line search; 65H10 -- 90C53; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2016.1274740
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: We present a new cubic convergent method for solving a system of nonlinear equations. The new method can be viewed as a modified Chebyshev's method in which the difference of Jacobian matrixes replaces three order tensor. Therefore, the new method reduces the storage and computational cost. The new method possesses the local cubic convergence as well as Chebyshev's method. A rule is deduced to ensure the descent property of the search direction, and a nonmonotone line search technique is used to guarantee the global convergence. Numerical results indicate that the new method is competitive and efficient for some classical test problems.