Taylor expansion of the accumulated rounding error. Linnainmaa, S. BIT, 16(2):146–160, BIT Computer Science and Numerical Mathematics, USA, June, 1976.
doi  abstract   bibtex   
The article describes analytic and algorithmic methods for determining the coefficients of the Taylor expansion of an accumulated rounding error with respect to the local rounding errors, and hence determining the influence of the local errors on the accumulated error. Second and higher order coefficients are also discussed, and some possible methods of reducing the extensive storage requirements are analyzed.
@article{linnainmaa1976taylor,
    author = {Linnainmaa, S.},
    title = {Taylor expansion of the accumulated rounding error},
    year = {1976},
    issue_date = {Jun 1976},
    publisher = {BIT Computer Science and Numerical Mathematics},
    address = {USA},
    volume = {16},
    number = {2},
    issn = {0006-3835},
    doi = {10.1007/BF01931367},
    abstract = {The article describes analytic and algorithmic methods for determining the coefficients of the Taylor expansion of an accumulated rounding error with respect to the local rounding errors, and hence determining the influence of the local errors on the accumulated error. Second and higher order coefficients are also discussed, and some possible methods of reducing the extensive storage requirements are analyzed.},
    journal = {BIT},
    month = jun,
    pages = {146–160},
    numpages = {15},
    keywords = {Storage Requirement, Local Error, Taylor Expansion, Rounding Error, Computational Mathematic},
    % url = {https://doi.org/10.1007/BF01931367},
}

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