Explicit solution of the polynomial least-squares approximation problem on Chebyshev extrema nodes

In this paper we propose an explicit solution to the polynomial least squares approximation problem on Chebyshev extrema nodes. We also show that the inverse of the normal matrix on this set of nodes can be represented as the sum of two symmetric matrices: a full rank matrix which admits a Cholesky factorization and a 2-rank matrix. Finally we discuss the numerical properties of the proposed formulas.