A New Method Of Multi-construct Of Lagrange Polynomial Interpolation

The multivariate polynomial interpolation problem is the core issue of computational mathematics, which is widely used and applied to many scientific fields. In 1965, the only solvability of the multivariate Lagrange interpolation problem is converted to a geometry problem by Professor Liang Xuezhang in [1] for the first time , so we can make use of the algebraic geometry approach to studying the only solvability of multivariate polynomial interpolation and the construction methods. Add a straight line and add the cone curve are given which can guarantee the unisolvence of multivariate polynomial interpolation, which makes the multiple problems of Lagrange interpolation with new breakthroughs and progress . In1977, K.C.CHUNG and T.H.YAO firstly make a point set to meet the concept of GC condition and prove a point set selected from the natural order simplex grid that can meet the GC condition, the point set is able to make unique interpolation polynomial exist. The main conclusions of this paper is based on the theory of GC condition, the higher times the polynomial interpolation meets QGC condition is constructed. The first part is introduction to the whole paper; in the second part, the theory of multivariate polynomial interpolation is introduced firstly; in the third part, the detailed description and discussion of the hot interpolation interpolation - Multivariate rational interpolation is given; in the fourth and final part, the GC condition is described and the QGC condition is proposed which proof and examples is given.