Semi Inherited Bivariate Interpolation

Abstract

The bivariate interpolation in two dimensional space $\mathbf{R}^2$ is more complicated than that in one dimensional space $\mathbf{R}$, because there is no Haar space of continuous functions in $\mathbf{R}^2$. Therefore, the bivariate interpolation has not a unique solution for a set of arbitrary distinct pairwise points. In this work, we suggest a type of basis which depends on the points such that the bivariate interpolation has the unique solution for any set of distinct pairwise points. In this case, the matrix of bivariate interpolation has the semi inherited factorization.