Local Convergence for a Regula Falsi-Type Method under Weak Convergence

[摘要] We present a local convergence analysis for a regula falsi-type method for solving nonlinear equations. In the earlier studies such as hypotheses on the second derivative have been used to show convergence of this method. In this paper we show convergence under hypotheses only on the first derivative. Moreover, we provide a radius of convergence and computable error bounds on the distances involved. Numerical examples are also given in this study.

[关键词] Regula falsi method;Radius of convergence;Local convergence