Computing sharp and scalable bounds on errors in approximate zeros of univariate polynomials
<|reference_start|>Computing sharp and scalable bounds on errors in approximate zeros of univariate polynomials: There are several numerical methods for computing approximate zeros of a given univariate polynomial. In this paper, we develop a simple and novel method for determining sharp upper bounds on errors in approximate zeros of a given polynomial using Rouche's theorem from complex analysis. We compute the error bounds using non-linear optimization. Our bounds are scalable in the sense that we compute sharper error bounds for better approximations of zeros. We use high precision computations using the LEDA/real floating-point filter for computing our bounds robustly.<|reference_end|>
@article{ramakrishna2003computing,
    title={Computing sharp and scalable bounds on errors in approximate zeros of
  univariate polynomials},
    author={P. H. D. Ramakrishna, Sudebkumar Prasant Pal, Samir Bhalla, Hironmay
  Basu and Sudhir Kumar Singh},
    journal={arXiv preprint arXiv:cs/0306015},
    year={2003},
    archivePrefix={arXiv},
    eprint={cs/0306015},
    primaryClass={cs.NA}
}