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A Unified Local Convergence for Two-Step Newton-Type Methods with High Order of Convergence under Weak Conditions |
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PP: 63-70 |
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doi:10.18576/sjm/050204
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Author(s) |
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Ioannis K. Argyros,
Santhosh George,
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Abstract |
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| We present a unified local convergence analysis for Newton-type methods in order to approximate a solution of a nonlinear
equation. In earlier studies such as [1,2,5]-[36] hypotheses of at least the third derivative have been used to show convergence. Our
local convergence is based on hypotheses up to the first derivative. This way, we expand the applicability of these methods. Moreover,
the radius of convergence, the uniqueness ball and computable error bounds involving Lipschitz constants not given before are also
provided in this study. Special cases and numerical examples are also given in this study. |
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