journal6 ›› 2008, Vol. 29 ›› Issue (1): 18-21.

• Mathematics • Previous Articles     Next Articles

Geometric Characterization for Bivariate Interpolation and Plane Configurations of Interpolation Nodes


  1. (School of Mathematics,Liaoning Normal University,Dalian 116029,Liaoning China)
  • Online:2008-01-25 Published:2012-05-26

Abstract: The existence and uniqueness of solution of bivariate interpolation problems are determined by the geometric characterization (GC) of a set of interpolation nodes.By means of the introduced concept defect,the sets satisfying the GC5 condition are discussed in this paper and geometric plane configurations of the conjecture are obtained when n=5.The constructed bivariate Lagrange formula can finally be expressed as a product of linear factors,through which the correctness of the conjecture is verified.

Key words: bivariate interpolation, interpolation nodes;geometric characterization;GCn set, defect

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