One-dimensional P-algorithm with convergence rate O(n-3+δ) for smooth functions

Algorithms based on statistical models compete favorably with other global optimization algorithms as shown by extensive testing results. A theoretical inadequacy of previously used statistical models for smooth objective functions was eliminated by the authors who, in a recent paper, have constructed a P-algorithm for a statistical model for smooth functions. In the present paper, a modification of that P-algorithm with an improved convergence rate is described.