Rational interpolation and quadrature on the interval and on the unit circle
نویسندگان
چکیده
Given a positive bounded Borel measure μ on the interval [−1, 1], we provide convergence results in Lμ2 -norm to a function f of its sequence of rational interpolating functions at the nodes of rational Gauss-type quadrature formulas associated with the measure μ. As an application, we construct rational interpolatory quadrature formulas for complex bounded measures σ on the interval, and give conditions to ensure the convergence of these quadrature rules. Further, an upper bound for the error on the nth approximation and an estimate for the rate of convergence is provided for these quadrature rules. Additionally, we briefly give similar results for certain rational interpolatory quadrature formulas associated with measures supported on the complex unit circle.
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