@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 = {

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.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/10221.html} }