王秀莲
(天津师范大学 数学科学学院,天津 300387)
拟Grünwald插值在Wiener空间下的平均误差
王秀莲
(天津师范大学 数学科学学院,天津 300387)
讨论改进的拟Grünwald插值在Wiener空间下的平均误差,得到了其于Lp范数意义下p-平均误差的弱渐近阶,证明了其于Lp范数意义下是收敛算子列.
Chebyshev多项式;拟Grünwald插值;Lp范数;Wiener空间
[1] Traub J F,Wasilkowski G W,Wozniakowski H.Information-based Complexity[M].New York:Academic Press,1988.
[2] Ritter K.Approximation and optimization on the Wiener space[J].J Complexity,1990,6(4):337-364.
[3] Hickernell F J,Wozniakowski H.Integration and approximation in arbitrary dimensions[J].Adv Comput Math,2000,12(1):25-58.
[4] Kon M,Plaskota L.Information-based nonlinear approximation:An average case setting[J].J Complexity,2005,21(2):211-229.
[5] Du Y F,Zhao H J.The average errors for the Grünwald interpolation in the Wiener space[J].Discrete Dynamics in Nature and Society,2009,10:1155-1166.
[6] 赵华杰,刘颖.Wiener空间中拟Grünwald插值的平均误差[J].天津师范大学学报:自然科学版,2008,28(2):48-53.
[7] Ritter K.Average-case Analysis of Numerical Problems[M].Berlin:Springer-Verlag,2000.
Average errors of quasi-Grünwald interpolation on Wiener space
WANGXiulian
(College of Mathematical Science,Tianjin Normal University,Tianjin 300387,China)
The average errors of modified quasi-Grünwald interpolation are discussed on Wiener space and weakly asymptotic order for thep-average errors ofLp-norm approximation is obtained.It is proved that the quasi-Grünwald interpolation sequence is convergence operator sequence forL p-norm approximation.
Chebyshev polynomials;quasi-Grünwald interpolation;Lp-norm;Wiener space
O174.41
A
1671-1114(2011)01-0025-04
2009-09-20
王秀莲(1965—),女,副教授,主要从事概率统计方面的研究.
(责任编校 马新光)