For solving least squares approximation problem simply and effectively on triangular domains in CAGD,this paper derives the matrices of transformation of the bivariate Bernstein basis form into the Jacobi basis of the same degree and vice versa.

Some Jacobians of the Transformation between Random Vectors and Matrices;

This involves computing the Jacobians of these transformations.

Then it can get a kind of model that has concentration weight and calculates the frequency with JACOBI method.

Weighted L_p~ω approximation by modified Bernstein-Durrmeyer operator with Jacobi weight;

Using the relation between the weighted modulus of smoothness and the weighted main-part modulus of smoothness,we discuss the pointwise direct and equivalent approximation theorem with Jacobi weight for Beta operator.

Using the moduli of smoothnessω_φ~Tλ(f,t)_ω,direct and inverse approximation theorems with Jacobi weight for combinations of Baskakov operators is established in the paper, and the relation between higher derivatives of the operators and the smoothness of functions to be approximated is obtained in the paper.

Some methods and skills in the implementation of the Jacobi sum primality testing;