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In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of ''N'', its subsequence ''x''1, ..., ''x''''N'' has a low discrepancy. Roughly speaking, the discrepancy of a sequence is low if the proportion of points in the sequence falling into an arbitrary set ''B'' is close to proportional to the measure of ''B'', as would happen on average (but not for particular samples) in the case of an equidistributed sequence. Specific definitions of discrepancy differ regarding the choice of ''B'' (hyperspheres, hypercubes, etc.) and how the discrepancy for every B is computed (usually normalized) and combined (usually by taking the worst value). Low-discrepancy sequences are also called quasi-random or sub-random sequences, due to their common use as a replacement of uniformly distributed random numbers. The "quasi" modifier is used to denote more clearly that the values of a low-discrepancy sequence are neither random nor pseudorandom, but such sequences share some properties of random variables and in certain applications such as the quasi-Monte Carlo method their lower discrepancy is an important advantage. ==Applications== Subrandom numbers have an advantage over pure random numbers in that they cover the domain of interest quickly and evenly. They have an advantage over purely deterministic methods in that deterministic methods only give high accuracy when the number of datapoints is pre-set whereas in using subrandom numbers the accuracy improves continually as more datapoints are added. Two useful applications are in finding the characteristic function of a probability density function, and in finding the derivative function of a deterministic function with a small amount of noise. Subrandom numbers allow higher-order moments to be calculated to high accuracy very quickly. Applications that don't involve sorting would be in finding the mean, standard deviation, skewness and kurtosis of a statistical distribution, and in finding the integral and global maxima and minima of difficult deterministic functions. Subrandom numbers can also be used for providing starting points for deterministic algorithms that only work locally, such as Newton–Raphson iteration. Subrandom numbers can also be combined with search algorithms. A binary tree Quicksort-style algorithm ought to work exceptionally well because subrandom numbers flatten the tree far better than random numbers, and the flatter the tree the faster the sorting. With a search algorithm, subrandom numbers can be used to find the mode, median, confidence intervals and cumulative distribution of a statistical distribution, and all local minima and all solutions of deterministic functions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Low-discrepancy sequence」の詳細全文を読む スポンサード リンク
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