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Volume 12, Issue 1
On the Convergence of the Brent Method

De-Ren Wang & Zhi-Jian Huang

J. Comp. Math., 12 (1994), pp. 1-20.

Published online: 1994-12

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  • 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.  

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@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} }
TY - JOUR T1 - On the Convergence of the Brent Method AU - Wang , De-Ren AU - Huang , Zhi-Jian JO - Journal of Computational Mathematics VL - 1 SP - 1 EP - 20 PY - 1994 DA - 1994/12 SN - 12 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/10221.html KW - AB -

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.  

De-Ren Wang & Zhi-Jian Huang. (1970). On the Convergence of the Brent Method. Journal of Computational Mathematics. 12 (1). 1-20. doi:
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