Improved convergence analysis of the Secant method using restricted convergence domains with real-world applications

In this paper, we are concerned with the problem of approximating a solution of a nonlinear equations by means of using the Secant method. We present a new semilocal convergence analysis for Secant method using restricted convergence domains. According to this idea we find a more precise domain where the inverses of the operators involved exist than in earlier studies. This way we obtain smaller Lipschitz constants leading to more precise majorizing sequences. Our convergence criteria are weaker and the error bounds are more precise than in earlier studies. Under the same computational cost on the parameters involved our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Different real-world applications are also presented to illustrate the theoretical results obtained in this study.