Explicit solution of the polynomial least-squares approximation problem on Chebyshev extrema nodes
The paper presents an explicit solution to the polynomial least squares approximation problem on Chebyshev extrema nodes. It is shown that the inverse of the normal matrix on the given 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. Further, an efficient algorithm is developed and studied. The numerical properties of the proposed algorithm are thoroughly discussed. Several numerical experiments are carried out to confirm and illustrate that the proposed algorithm is fast and accurate.
scientific article; zbMATH DE number 5141634