Reliability Conditions in Quadrature Algorithms
<|reference_start|>Reliability Conditions in Quadrature Algorithms: The detection of insufficiently resolved or ill-conditioned integrand structures is critical for the reliability assessment of the quadrature rule outputs. We discuss a method of analysis of the profile of the integrand at the quadrature knots which allows inferences approaching the theoretical 100% rate of success, under error estimate sharpening. The proposed procedure is of the highest interest for the solution of parametric integrals arising in complex physical models.<|reference_end|>
@article{adam2003reliability,
    title={Reliability Conditions in Quadrature Algorithms},
    author={Gh. Adam, S. Adam, and N.M. Plakida},
    journal={arXiv preprint arXiv:cs/0303004},
    year={2003},
    doi={10.1016/S0010-4655(03)00282-0},
    number={E17-2002-205 (JINR Dubna preprint, sept.2002; preliminary version of
  this paper)},
    archivePrefix={arXiv},
    eprint={cs/0303004},
    primaryClass={cs.NA cs.MS physics.comp-ph}
}