Abstract
Leap-frogging Newton’s method is constructed by combining the classical Newton’s method with the pseudo-secant method. Under the assumptions that a given function f : R → R has a simple real zero α and is sufficiently smooth in a small neighborhood of α, we investigate the convergence behavior of Leap-frogging Newton’s method near α. The order of convergence is shown to be cubic and the asymptotic error constant is proven to be 1 4 · f ″ ( α ) f ′ ( α ) 2 . The numerical method based on this proposed theory have shown satisfactory results via programming in Mathematica with its high-precision computability.
Sign-in/Register to access full text options 
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 callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
