Upper bound evaluation in function recovery by linear method in the Besov space

Manh Cuong Nguyen1,
1 Kien Giang University, Vietnam

Main Article Content

Abstract

This paper studies recovery and approximation of functions in the Besov spaces with mixed smoothness by linear methods. Accordingly, linear sampling recovery methods of functions are conducted in the Besov spaces and the upper bound of the method is evaluated. The main result of this paper is to extend and generalize the previous results.

Article Details

References

Chui, C. K. (1992). An Introduction to Wavelets, Academic Press, New York.
DeVore, R. A., & Lorentz G. G. (1993). Constructive approximation, Springer, Berlin.
Dinh, D. (2000), Continous algorithms in n-term approximation and nonlinear widths. J. Approx. Theory, 102, 217-242.
Dinh, D. (2001). Non-linear approximations using sets of finite cardinality or finite pseudo- dimension. J. Complexity., 17, 467-492.
Dinh, D. (2009). Non-linear sampling recovery based on quasi-interpolant wavelet representations. Adv. in Comput. Math., 30, 375-401.
Dinh, D. (2011a). B-spline quasi-interpolant representations and sampling recovery of functions with mixed smoothness. J. Complex., 27, 541-567.
Dinh, D. (2011b). Optimal adaptive sampling recovery, Adv. in Comput. Math., 34, 1-41.
Dinh, D. (2016). Sampling and cubature on sparse grids based on a B-spline quasi-interpolation. Found. Comp. Math., 16, 1193-1240.
Nguyen, C. M., & Mai, T. X.(2018). Quasi-interpolation representation and sampling recovery of multivariate functions. Acta Math. Vietnamica, 43, 373-389.
Nguyen, C. M. (2019). Nonlinear approximations of functions having mixed smoothness. J. Comput. Sci. Cybern., 35, 119-134.
Nguyen, C. M. (2021). Adaptive sampling recovery and nonlinear approximations of multivariate functions in Besov-type spaces. Southeast Asian Bull. Math., 45, 461-482.
Nikol'skii, S. (1975). Approximation of Functions of Several Variables and Embedding Theorems. Springer Verlag, Berlin.
Temlyakov, V. (1993). Approximation of periodic functions. Nova Science Publishers, Inc., New York.
Temlyakov, V. (1985). Approximation recovery of periodic functions of several variables. Mat. Sb., 128, 256–268.