@Article{JCM-12-1,
author = {Wang , De-Ren and Huang , Zhi-Jian},
title = {On the Convergence of the Brent Method},
journal = {Journal of Computational Mathematics},
year = {1994},
volume = {12},
number = {1},
pages = {1--20},
abstract = {<p style="text-align: justify;">In this paper, we establish the semi-local convergence theorem of the Brent method with regional estimation. By an in-depth investigation in to the algorithm structure of the method, we convert the Brent method into an approximate Newton method with a special error term. Based on such equivalent variation, under a similar condition of the Newton-Kantorovich theorem of the Newton method, we establish a semi-local convergence theorem of the Brent method. This theorem provides a sufficient theoretical basis for initial choices of the Brent method. &nbsp;</p>},
issn = {1991-7139},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jcm/10221.html}
}