Universality in numerical computations with random data

Percy Deift, Govind Menon, Sheehan Olver, Thomas Trogdon

Research output: Contribution to journalArticle

Abstract

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 aswell 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.

Original languageEnglish (US)
Pages (from-to)14973-14978
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Volume111
Issue number42
DOIs
StatePublished - Oct 21 2014

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Numerical Computation
Universality
Sample variance
Numerical Algorithms
Stochastic Algorithms
Data Distribution
Histogram
Tolerance
Random variable
Decision Making
Fluctuations
Statistics
Iteration
Curve
Software
Model

Keywords

  • Decision times
  • Numerical analysis
  • Random matrix theory

ASJC Scopus subject areas

  • General

Cite this

Universality in numerical computations with random data. / Deift, Percy; Menon, Govind; Olver, Sheehan; Trogdon, Thomas.

In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 111, No. 42, 21.10.2014, p. 14973-14978.

Research output: Contribution to journalArticle

Deift, Percy ; Menon, Govind ; Olver, Sheehan ; Trogdon, Thomas. / Universality in numerical computations with random data. In: Proceedings of the National Academy of Sciences of the United States of America. 2014 ; Vol. 111, No. 42. pp. 14973-14978.
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