The Rate of Lp,Convergence of the Grǖnwald Process
Received:July 27, 1998  
Key Words: Tchebycheff polynomials   Grǖnwald interpolatory process   modified Grǖnwald interpolatory process   moduli of smoothness.  
Fund Project:
Author NameAffiliation
XU Gui-qiao Dept.of Math.
Beijing Normal University
China 
LIU Yong-ping Dept.of Math.
Beijing Normal University
China 
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Abstract:
      The Lp-convergence properties of the Grǖnwald process based on the second kind Tchebycheff nodes are discussed.When 1≤p < 2 ,an accurate bound of first convergence rate is given.When p≥2 ,that they aren't Lp,-convergenceo perators sequence is shown. We also give a kind of modified Grunwald process based on the second kind Tchebycheff nodes,and we discuss first Lp-convergence properities for 1≤P<∞ .
Citation:
DOI:10.3770/j.issn:1000-341X.2001.03.025
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