Average errors for zero finding: Lower bounds for smooth or monotone functions
An error analysis of zero finding for monotone or \(C^ r(0; I)\) functions is presented. The errors for methods using \(n\) function or derivative evaluations are defined with respect to \(r\)-fold Wiener or Ulam measures and are understood in the root or residual sense. The author shows that it is impossible to obtain superlinear convergence even for classes of smooth functions which have only simple zeros. Besides new results, the article presents a good introduction to the problem.
scientific article; zbMATH DE number 699777
scientific article