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- W3145533421 abstract "In this paper,we present the methods of construction of quaternary orthonormal system (so-called QU-system) with piecewise polynomials,discuss the feasibility of the construction methods,and obtain a set of explicit expressions of QU-system with degrees 1 to 3.And then,we investigate the properties of QU-system and the relationship between binary U-system and QU-system,and present the formulae of its basis value and Fourier-QU coefficient.Applying the investigated construction methods,we can construct a class of complete orthonormal system in L2[0,1],which contains both continuous and discontinuous piecewise polynomials.So QU-system has the properties of both Fourier trigonometric functions and Walsh functions.Finally,we apply numerical experiments to confirm that the convergence rate of Fourier-QU series is better than that of Fourier series,Walsh series and Fourier-BU series,if using the first finite terms of them to approximate the functions of one variable." @default.
- W3145533421 created "2021-04-13" @default.
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- W3145533421 date "2011-01-01" @default.
- W3145533421 modified "2023-09-25" @default.
- W3145533421 title "A class of quaternary orthonormal U-system" @default.
- W3145533421 hasPublicationYear "2011" @default.
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