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We present a tighter convergence analysis than earlier studies such as in Cianciaruso (2007), Guo (2007), Shen and Li (2010), Smale (1986, 1987), Wang and Zhao (1995), Wang (1999), Wang and Han (1990) of Newton’s method using Smale’s α-theory by introducing the notion of the center γ0-condition. In particular, in the semilocal convergence case we show that if the center γ0-condition is smaller than...
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