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Efficient Simulation of Random Fields by Trigonometric Polynomial and Low‐rank Tensor
Author(s) -
Liu Dishi,
Vondřejc Jaroslav,
Matthies Hermann
Publication year - 2021
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.202000341
Subject(s) - rank (graph theory) , tensor (intrinsic definition) , mathematics , discretization , trigonometric polynomial , trigonometry , fast fourier transform , random field , representation (politics) , field (mathematics) , tensor field , polynomial , pure mathematics , mathematical analysis , combinatorics , algorithm , exact solutions in general relativity , statistics , politics , political science , law
We propose a fast and economic representation of stationary random fields in trigonometric polynomial, utilizing the prowess of fast Fourier transform (FFT) and low‐rank tensor approximation. With the method we are able to generate large random fields with discretization size up to 2 20 which are otherwise well beyond the capacity of PCs. We also illustrate the approach to the specified property of random field by increasing rank in the tensor approximation.