On the local convergence of fast two-step Newton-like methods for solving nonlinear equations

• Published in: Journal of computational and applied mathematics Vol. 245; pp. 1 - 9
• Main Authors: Argyros, I.K., Hilout, S.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-06-2013
• Subjects: Banach space; Chebyshev approximation; Chebyshev’s method; Computation; Convergence; Mathematical models; Newton methods; Newton-like method; Newton’s method; Nonlinear equations; Secant method; Semilocal convergence; Semilocal convergence; 47H99; Chebyshev’s method; Secant method; Newton’s method; 65G99; 49M15; Banach space; Newton-like method; 65J15
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2012.12.002

A local convergence analysis is presented for a fast two-step Newton-like method (TSNLM) for solving nonlinear equations in a Banach space setting. The TSNLM unifies earlier methods such as Newton’s, Secant, Newton-like, Chebyshev–Secant, Chebyshev–Newton, Steffensen, Stirling’s and other single or multistep methods. Numerical examples and a comparative study of these methods validating our theoretical results are also given in the concluding section of this paper.