JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (10): 11-15.doi: 10.6040/j.issn.1671-9352.0.2015.541

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The average error of linear tensor product multivariate polynomial interpolation based on Chebyshev nodes on the Brownian sheet measure

XIONG Li-yan, XU Gui-qiao*   

  1. College of Mathematical Science, Tianjin Normal University, Tianjin 300387, China
  • Received:2015-11-18 Online:2016-10-20 Published:2016-10-17

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Abstract: Based on univariate Lagrange polynomial interpolation, a kind of linear tensor product polynomial interpolation is constructed to approximate multivariate functions. For the weighted L2-norm,their average errors is studied on the Brownian sheet measure and obtained the corresponding stronger asymptotic order. Compared with the past algorithms based on linear functional information, our algorithms are based on standard information and it is constructive. It can also be applied to solve practical problems. From the perspective of average error, it is showed that algorithms are order optimal to the univariate function case setting, and have a similar approximation order to the optimal algorithms based on linear functional information to the multivariate function case setting.

Key words: Chebyshev nodes, average error, weighted L2-norm, Brownian sheet measure

CLC Number: 

  • O174.41
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