Optimal asymptotic Lebesgue constant of Berrut’s rational interpolation operator for equidistant nodes

摘要

In approximation theory, the Lebesgue constant of an interpolation operator plays an important role. The Lebesgue constant of Berrut’s interpolation operator has been extensive studied. In the present work, by introducing a new method, we obtain an optimal asymptotic Lebesgue constant of Berrut’s rational interpolant at equidistant nodes.