Rounding probabilities: Maximum probability and minimum complexity multipliers
The aim of the paper is to study four multipliers that are used in multiplier techniques of rounding theory based on rounding functions. In order to make the discrepancy close to zero, a good choice of multiplier is essential. The paper defines the four multipliers and shows their asymptotic equivalence behaviour. Section 2 reviews the authors' earlier results on the so-called ``easy-to-calculate'' multipliers, and the exactly unbiased multiplier. Sections 3 and 4 introduce the maximum probability (to vanishing discrepancy) multiplier, and the minimum complexity multiplier (that minimizes the expectation of the absolute value of discrepancy). Section 5 is devoted to the asymptotic discrepancy distribution, and the final Section 6 strongly recommend the ``easy-to-calculate'' multiplier since, asymptotically, it bears also the qualities of the other three multipliers, i.e. it achieves unbiasedness, maximizes the probability of a vanishing discrepancy, and minimizes the complexity of the generic rounding algorithm.
scientific article; zbMATH DE number 1436936