A modified least squares method: Approximations on the unit circle and on (−1,1)

Abstract

The main objective in the present manuscript is to consider approximations of functions defined on the unit circle by Laurent polynomials derived from certain combinations of kernel polynomials of orthogonal polynomials on the unit circle. The method that we employ is based on a modification of the least squares method. The modification adopted here simplifies considerably the determinations of the coefficients in the combinations. Numerical examples show that this modified technique still leads to very good approximations.