Classifying extrema using intervals
<|reference_start|>Classifying extrema using intervals: We present a straightforward and verified method of deciding whether the n-dimensional point x (n>=1), such that \nabla f(x)=0, is the local minimizer, maximizer or just a saddle point of a real-valued function f.   The method scales linearly with dimensionality of the problem and never produces false results.<|reference_end|>
@article{gutowski2006classifying,
    title={Classifying extrema using intervals},
    author={Marek W. Gutowski},
    journal={arXiv preprint arXiv:cs/0609082},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0609082},
    primaryClass={cs.MS cs.CC cs.NA}
}