Semi Inherited Bivariate Interpolation

Abstract

The bivariate interpolation in two dimensional space R 2 is more complicated than that in one dimensional space R, because there is no Haar space of continuous functions in 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.

Inherited collocation method for fuzzy differential equations

“…Then, the LU factorization of matrices is applied to decompose the extended system of linear equations with crisp coefficients in a simple manner. Inherited basis functions was introduced by the authors in [16,17]. Also, the inherited LU factorization was applied for solving fuzzy system of linear equations in [18].…”