zbMATH — the first resource for mathematics

On the convergence of the secant method in Banach space. (Chinese. English summary) Zbl 1013.65051
Summary: We weaker conditions is given for the convergence of the secant method than that the paper by M. A. Hernández and M. J. Rubio [\((*)\) Int. J. Comput. Math. 72, No. 4, 477-490 (1999; Zbl 0967.65073)] by using the same information at initial points used in \((*)\). A similar error estimate is also given as that in \((*)\). At the same time, the error estimate of \({\|f(x_{n+1})\|\over\|f(x_n)\|}\) is obtained.

65J15 Numerical solutions to equations with nonlinear operators (do not use 65Hxx)
47J25 Iterative procedures involving nonlinear operators