拟Grünwald插值在Wiener空间下的平均误差

2011-01-06 09:15王秀莲
关键词:天津师范大学编校范数

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)

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