Journal article
Non-periodic Multivariate Stochastic Fourier Sine Approximation and Uncertainty Analysis
Journal of computational analysis and applications, Vol.22(4), pp.754-775
04/01/2017
Abstract
In data analysis, one needs to study Fourier sine analysis on the unit cube. However, for this kind of non-periodic case, no exact result is available. In this paper, firstly, based on our multivariate function decomposition, we deduce an asymptotic formula of Fourier sine coefficients of continuously differentiable functions f on [0, 1](d). Secondly, we deduce an asymptotic formula of hyperbolic cross approximations of Fourier sine series of f on [0, 1](d). By this way we can reconstruct high-dimensional signals by using fewest Fourier sine coefficients. Thirdly, we extend these results to Fourier sine analysis of stochastic processes and give uncertainty of stochastic Fourier sine approximation, i.e., we obtain expectations and variances of stochastic Fourier sine coefficients and stochastic Fourier sine approximation errors. Finally, we discuss some known stochastic processes.
Details
- Title: Subtitle
- Non-periodic Multivariate Stochastic Fourier Sine Approximation and Uncertainty Analysis
- Creators
- Zhihua Zhang - Beijing Normal UniversityPalle E. T Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Journal of computational analysis and applications, Vol.22(4), pp.754-775
- Publisher
- EUDOXUS PRESS, LLC
- ISSN
- 1521-1398
- eISSN
- 1572-9206
- Number of pages
- 22
- Grant note
- Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry 105565GK / Fundamental Research Funds for the Central Universities (Key Program) 2013CB956604 / National Key Science Program Beijing Young Talent fund
- Language
- English
- Date published
- 04/01/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984240861402771
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