A family of 2n-point approximating subdivision schemes based on least squares method

Abstract

In this paper, a procedure to construct a family of 2n-point approximating subdivision schemes is presented for an integer n > 4. Firstly, a least squares technique has been used to fit a polynomial of degree seven to data. Secondly, a family of 2n-point subdivision scheme is constructed. In particular, some important features of first three members of the family of 2n-point schemes are also discussed. Geometric performances of some members of the family are shown with the help of several examples.