Rational interpolation: I. Least square convergence

Given a positive bounded Borel measure μμ on the interval [−1,1][−1,1], we provide convergence results in L2μ-norm to a function ff of its sequence of interpolating rational functions at the nodes of rational Gauss-type quadrature formulas associated with the measure μμ. For this, we use the connection between rational Gauss-type quadrature formulas on [−1,1][−1,1] and rational Szegő quadrature formulas associated with a positive symmetric Borel measure μ̊ on the complex unit circle.