Year: 1994
Author: De-Ren Wang, Zhi-Jian Huang
Journal of Computational Mathematics, Vol. 12 (1994), Iss. 1 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1994-JCM-10221
Journal of Computational Mathematics, Vol. 12 (1994), Iss. 1 : pp. 1–20
Published online: 1994-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20