A novel recursive method to reconstruct multivariate functions on the unit cube

• Autorzy: Zhihua Zhang
• Języki publikacji: EN

Abstrakty

EN

Due to discontinuity on the boundary, traditional Fourier approximation does not work efficiently for d−variate functions on [0, 1]d. In this paper, we will give a recursive method to reconstruct/approximate functions on [0, 1]d well. The main process is as follows: We reconstruct a d−variate function by using all of its (d−1)–variate boundary functions and few d–variate Fourier coefficients. We reconstruct each (d−1)–variate boundary function given in the preceding reconstruction by using all of its (d−2)–variate boundary functions and few (d−1)–variate Fourier coefficients. Continuing this procedure, we finally reconstruct each univariate boundary function in the preceding reconstruction by using values of the function at two ends and few univariate Fourier coefficients. Our recursive method can reconstruct multivariate functions on the unit cube with much smaller error than traditional Fourier methods.

Słowa kluczowe

EN

Recursive method; Hyperbolic cross truncation; Multivariate functions; Fourier series

Kategorie tematyczne

• 42B05: Fourier series and coefficients
• 41A63: Multidimensional problems (should also be assigned at least one other classification number in this section)

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2017
• Tom: 15
• Numer: 1
• Strony: 1568-1577

Daty

wydano

2017-01-01

otrzymano

2016-11-03

zaakceptowano

2017-11-16

online

2017-12-29

Twórcy

autor

Zhihua Zhang

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Identyfikatory

DOI

10.1515/math-2017-0132