Calculation of the maximum value of a twice-differentiable function with a posteriori error estimate (Q1074312)

We describe a sequential algorithm that computes the function at the same points as does the algorithm of the author and \textit{S. B. Vasil'ev} [ibid. 31, 312-315 (1982; Zbl 0514.65052)], but, as a result of more complete utilization of the information about the computed values, provides a better approximation to \(f^*\) than the preassigned accuracy \(\epsilon\). The algorithm is a recurrence procedure that does not demand storage of all the previously computed values in order to perform the next step (including the last).