Increasing reliability of Gauss–Kronrod quadrature by Eratosthenesʹ sieve method Original Research Article

The reliability of the local error estimates returned by the Gauss–Kronrod quadrature rules can be raised up to the theoretical 100% rate of success, under error estimate sharpening, provided a number of natural validating conditions are required. The self-validating scheme of the local error estimates, which is easy to implement and adds little supplementary computing effort, strengthens considerably the correctness of the decisions within the automatic adaptive quadrature.