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