Multivariate Polynomial Interpolation Based on the Partition of Concentric Circles and Lines

Many traditional interpolation methods are based on the triangular and quadrilateral partition.These approaches have drawback when they are applied to deal with problems of circular distribution.This paper presents a new method to construct the multivariate polynomial interpolation based on the partition of concentric circles and lines. The data points are distributed circularly,and the basis functions are symmetrical,thus the interpolation function preserves symmetry and it is polynomial.Examples are given to illustrate the efficiency of interpolation,and the error analysis is also included.