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Universality in numerical computations with random data
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DOI：10.1073/pnas.1413446111.png)
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摘要
En 中文
The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance) is a random variable, called the halting time. Two-component universality is observed for the fluctuations of the halting time-i.e., the histogram for the halting times, centered by the sample average and scaled by the sample variance, collapses to a universal curve, independent of the input data distribution, as the dimension increases. Thus, up to two components-the sample average and the sample variance-the statistics for the halting time are universally prescribed. The case studies include six standard numerical algorithms as well as a model of neural computation and decision-making. A link to relevant software is provided for readers who would like to do computations of their own.
Keyword:
random matrix theory
decision times
numerical analysis
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期刊
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IF:
9.1
论文数:
10.8W
被引数:
73.5W
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