The convergence rate of the sandwich algorithm for approximating convex functions (Q1195962)

Interval bisection, slope bisection, maximum error rule and chord rule are considered as four natural rules leading to different versions of the sandwich algorithm for approximating a convex function of one variable over an interval by evaluating the function and its derivative at a sequence of points. Further the author demonstrates that the global approximation error with \(n\) evaluation points decreases by the order of \(O(1/n^ 2)\) which is optimal.