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Argyros, Ioannis K.; Hilout, Saïd

Convergence of directional methods under mild differentiability and applications. (English) Zbl 1223.65035

Appl. Math. Comput. 217, No. 21, 8731-8746 (2011).
This paper deals with the convergence analysis of the directional Newton method (DNM) for approximating a zero of a differentiable function defined on a convex set. A semilocal convergence analysis for DNM is provided. Some sufficient conditions on convergence as well as the corresponding error bounds are provided. Several previous results are extended or improved.
Reviewer: Liu Xinguo (Qingdao)

Cited in 2 Documents

MSC:

65H10 Numerical computation of solutions to systems of equations

Keywords:

directional Newton method; systems of nonlinear equations; convergence; error bounds; Hilbert space; Banach space; zero of a differentiable function; semilocal convergence
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References:

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