The weighted dual functions for Wang–Bézier type generalized Ball bases and their applications

By introducing the inner-product matrix of two vector functions and using conversion matrix, explicit formulas for the dual basis functions of Wang-Bezier type generalized Ball bases (WBGB) with respect to the Jacobi weight function are given. The dual basis functions with and without boundary constraints are also considered. As a result, the paper includes the weighted dual basis functions of Bernstein basis, Wang-Ball basis and some intermediate bases. Dual functionals for WBGB and the least square approximation polynomials are also obtained.