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Journal of Zhejiang University SCIENCE A 2003 Vol.4 No.1 P.80-85


On the approximate zero of Newton method

Author(s):  HUANG Zheng-da

Affiliation(s):  Department of Mathematics, Zhejiang University, Hangzhou 310028, China

Corresponding email(s):   huangzd@css.zju.edu.cn

Key Words:  Approximate zero, Newton method, Generalized Kantorovich Condition

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HUANG Zheng-da. On the approximate zero of Newton method[J]. Journal of Zhejiang University Science A, 2003, 4(1): 80-85.

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DOI - 10.1631/jzus.2003.0080

A judgment criterion to guarantee a point to be a Chen's approximate zero of newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen's approximate zero may not be a Smale's approximate zero. The error estimate obtained indicated the convergent order when we use |f(x)|<ε to stop computation in software. The result can also be applied for solving partial derivative and integration equations.

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