A Fully-Nested Interpolatory Quadrature Based on Fejer's Second Rule

摘要

Our goal is to alleviate the constraint of the classical 1D interpolatory nested quadratures than one should go from a set of n to a set of (2n + 1) points (for Fejer second rule) or (2n - 1) points (for Clenshaw-Curtis rule) to benefit from the nesting property. In this work a sequence of recursively included quadrature sets for all odd number of quadrature points is proposed to define interpolatory rules. These sets are confounded with the one of Fejer's second rule when the cardinal is a power of two minus one and different if not. The weights of the corresponding interpolatory rule are studied. This rule is efficient for calculating integrals of very regular functions with control of accuracy via application of successive formulas of increasing order.