Convergence of rational interpolatory quadrature rules

par Karl Deckers (Université de Lille)

jeudi 22 nov. 2012, 10:30 → 11:30 Europe/Paris

XR.203 (Bâtiment XLIM)

Consider an nth rational interpolatory quadrature rule J_n^\sigma(f)=\sum_{j=1}^n\lambda_jf(x_j) to approximate integrals of the form J_\sigma(f)=\int_{-1}^1f(x)d\sigma(x), where \sigma is a (possibly complex) bounded measure with infinite support on the interval [-1,1]. We then provide conditions to ensure the convergence of J_n^\sigma(f) to J_\sigma(f) for n tending to infinity. Further, an upper bound for the error on the nth approximation and an estimate for the rate of convergence is provided.