R-order of convergence for the improved multi-point Chebyshev-like methods under generalized continuity condition

AbstractIn this paper, the convergence for improved multi-point Chebyshev-like methods is considered. Compared to the results of Chebyshev method with second derivative in reference (M.A. Hernandez, M.A. Salanova, Journal of Computational and Applied Mathematics 126 (2000) 131-143), the R-order is maximised and the Holder continuity condition is also relaxed. Moreover, these improved methods do not need second derivatives, when the computation of second derivative is large, these improved methods will be more efficient than Chebyshev method. Under the relaxed condition, an existence-uniqueness theorem is proved. The R-order of convergence for these improved methods is also analyzed.