  In this article, families of non-linear subdivision schemes are presented
that are based on univariate polynomials up to degree three. Theses families of
schemes are constructed by using dynamic iterative re-weighed least squares
method. These schemes are suitable for fitting scattered data with noise and
outliers. Although these schemes are non-interpolatory, but have the ability to
preserve the shape of the initial polygon in case of non-noisy initial data.
The numerical examples illustrate that the schemes constructed by non-linear
polynomials give better performance than the schemes that are constructed by
linear polynomials (Computer-Aided Design, 58, 189-199). Moreover, the
numerical examples show that these schemes have the ability to reproduce
polynomials and do not cause over and under fitting of the data. Furthermore,
families of non-linear bivariate subdivision schemes are also presented that
are based on linear and non-linear bivariate polynomials.
