Increasing reliability of Gauss-Kronrod quadrature by Eratosthenes' sieve method

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 co nditions are required. The self-validating scheme of the local error estima tes, which is easy to implement and adds little supplementary computing eff ort, strengthens considerably the correctness of the decisions within the a utomatic adaptive quadrature. (C) 2001 Elsevier Science B.V. All rights res erved.