ON THE CONVERGENCE OF THE BRENT METHOD  

作　　者：WANG, DR HUANG, ZJ 

机构地区：[1]SHANGHAI UNIV SCI & TECHNOL,DEPT MATH,SHANGHAI,PEOPLES R CHINA [2]FUDAN UNIV,DEPT STAT & OPERAT RES,SHANGHAI,PEOPLES R CHINA

出　　处：《Journal of Computational Mathematics》1994年第1期1-20,共20页计算数学（英文）

摘　　要：In this paper, we establish the semi-local convergence theorem of the rent 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. Bsaed 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.In this paper, we establish the semi-local convergence theorem of the rent 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. Bsaed 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.

关 键 词：holds CHOICE VERGENCE CONVERGENT ELIMINATION otherwise Brent Dennis Cornell APPROXIMATE 

分 类 号：O24[理学—计算数学]