The Average Errors for Linear Combinations of Bernstein Operators on the Wiener Space*
Affiliation(s)
Department of Mathematics and Physics, North China Electric Power University, Baoding, China.
Department of Mathematics and Physics, North China Electric Power University, Baoding, China.
ABSTRACT
In this paper, we discuss the average errors of function approximation by linear combinations of Bernstein operators. The strongly asymptotic orders for the average errors of the combinations of Bernstein operators sequence are determined on the Wiener space.
Cite this paper
Y. Jiang and Z. Zhang, "The Average Errors for Linear Combinations of Bernstein Operators on the Wiener Space*," Journal of Data Analysis and Information Processing, Vol. 1 No. 4, 2013, pp. 85-89. doi: 10.4236/jdaip.2013.14009.
Y. Jiang and Z. Zhang, "The Average Errors for Linear Combinations of Bernstein Operators on the Wiener Space*," Journal of Data Analysis and Information Processing, Vol. 1 No. 4, 2013, pp. 85-89. doi: 10.4236/jdaip.2013.14009.
References
[1] K. Ritter, “Average-Case Analysis of Numerical Problems,” Springer-Verlag, Berlin, 2000. [2] P. L. Butzer, “Linear Combinations of Bernstein Polyno-mials,” Canadian Journal of Mathematics, Vol. 5, 1953, pp. 559-567. http://dx.doi.org/10.4153/CJM-1953-063-7 [3] Z. Ditzian and V. Totik, “Moduli of Smoothness,” Springer-Verlag, Berlin, 1987. http://dx.doi.org/10.1007/978-1-4612-4778-4 [4] G. Q. Xu, “The Simultaneous Approximation Average Errors for Bernstein Operators on the R-Fold Integrated Wiener Space,” Numerical Mathematics Theory Methods and Applications, Vol. 5, No. 3, 2012, pp. 403-422. [5] G. G. Lornetz, “Bernstein Polynomials,” University of Toronto, Toronto, 1953.
[1] K. Ritter, “Average-Case Analysis of Numerical Problems,” Springer-Verlag, Berlin, 2000. [2] P. L. Butzer, “Linear Combinations of Bernstein Polyno-mials,” Canadian Journal of Mathematics, Vol. 5, 1953, pp. 559-567. http://dx.doi.org/10.4153/CJM-1953-063-7 [3] Z. Ditzian and V. Totik, “Moduli of Smoothness,” Springer-Verlag, Berlin, 1987. http://dx.doi.org/10.1007/978-1-4612-4778-4 [4] G. Q. Xu, “The Simultaneous Approximation Average Errors for Bernstein Operators on the R-Fold Integrated Wiener Space,” Numerical Mathematics Theory Methods and Applications, Vol. 5, No. 3, 2012, pp. 403-422. [5] G. G. Lornetz, “Bernstein Polynomials,” University of Toronto, Toronto, 1953.