Geodesic
Convergence Ball Analysis of a Modified Newton's Method Under Hölder Continuous Condition in Banach Space
Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 1

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A modified Newton's method which computes derivatives every other step is used to solve a nonlinear operator equation. An estimate of the radius of its convergence ball is obtained under Hölder continuous Fréchet derivatives in Banach space. An error analysis is given which matches its convergence order.
Classification : 65B05, 47817, 49D15 
Qingbiao Wu; Hongmin Ren. Convergence Ball Analysis of a Modified Newton's Method Under Hölder Continuous Condition in Banach Space. Bulletin of the Malaysian Mathematical Society, Tome 36 (2013) no. 1. http://geodesic.mathdoc.fr/item/BMMS_2013_36_1_a22/
@article{BMMS_2013_36_1_a22,
     author = {Qingbiao Wu and Hongmin Ren},
     title = {Convergence {Ball} {Analysis} of a {Modified} {Newton's} {Method} {Under} {H\"older} {Continuous} {Condition} in {Banach} {Space}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2013},
     volume = {36},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2013_36_1_a22/}
}
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