Geodesic
Convergence of a continuous analog of Newton's method for solving nonlinear equations
Numerical methods and programming, Tome 10 (2009) no. 4, pp. 402-407.

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The influence of the parameter in the continuous analog of Newton's method (CANM) on the convergence and on the convergence rate is studied. A $\tau$-region of convergence of CANM for both scalar equations and equations in a Banach space is obtained. Some almost optimal choices of the parameter are proposed. It is also shown that the well-known higher order convergent iterative methods lead to the CANM with an almost optimal parameter. Several sufficient convergence conditions for these methods are obtained.
Keywords: iterative methods; rate of convergence; Newton-type methods; nonlinear equations. 
@article{VMP_2009_10_4_a6,
     author = {T. Zhanlav and O. Chuluunbaatar},
     title = {Convergence of a continuous analog of {Newton's} method for solving nonlinear equations},
     journal = {Numerical methods and programming},
     pages = {402--407},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2009_10_4_a6/}
}
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T. Zhanlav; O. Chuluunbaatar. Convergence of a continuous analog of Newton's method for solving nonlinear equations. Numerical methods and programming, Tome 10 (2009) no. 4, pp. 402-407. http://geodesic.mathdoc.fr/item/VMP_2009_10_4_a6/