Rational interpolation: I. Least square convergence

Given a positive bounded Borel measure µ on the interval [−1, 1], we provide con-vergence results in Lµ2-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 quadra-ture formulas on [−1, 1] and rational Szego ̋ quadrature formulas associated with a positive symmetric Borel measure µ ̊ on the complex unit circle. Key words: Orthogonal rational functions, rational interpolation, least square convergence.