Rational interpolation: I. Least square convergence

Given a positive bounded Borel measure μ on the interval [ − 1 , 1 ] , we provide convergence results in L 2 μ -norm to a function f of its sequence of interpolating rational functions at the nodes of rational Gauss-type quadrature formulas associated with the measure μ . For this, we use the connection between rational Gauss-type quadrature formulas on [ − 1 , 1 ] and rational Szegő quadrature formulas associated with a positive symmetric Borel measure μ ̊ on the complex unit circle.