Modeling of curves with parametric polynomials by the method of least squares

We consider the problem of the approximation of discrete functions with parametric polynomials by method of least squares (MLS). The problem of the choice of the best parameter is studied. The problem of the determination of coefficients of approximation polynomials is solved by the traditional method – solving the normal system of MLS, and by method of orthogonal polynomials. The presented algorithms can be applied to both space and plane curves.