@Article{JCM-12-1,
author = {Wang, De-Ren and Zhi-Jian, Huang},
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/1994-JCM-10221},
url = {https://global-sci.com/article/85836/on-the-convergence-of-the-brent-method}
}