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Kantorovich-type convergence criterion for inexact Newton methods. (English) Zbl 1165.65354
Summary: Assuming that the first derivative of an operator satisfies the Lipschitz condition, a Kantorovich-type convergence criterion for inexact Newton methods is established, which includes the well-known Kantorovich theorem as a special case. Comparisons and a numerical example are presented to illustrate that our results obtained in the present paper improve and extend some recent results in [X. P. Guo, J. Comput. Math. 25, No. 2, 231–242 (2007; Zbl 1142.65354); W. P. Shen and C. Li, Taiwanese J. Math. 12, No. 7, 1865–1882 (2008; Zbl 1170.65042)].
MSC:
65J15Equations with nonlinear operators (numerical methods)
65H10Systems of nonlinear equations (numerical methods)
47H30Particular nonlinear operators
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