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2007•Taiwanese Journal of MathematicsOpen access

THE CONVERGENCE BALL OF NEWTON-LIKE METHODS IN BANACH SPACE AND APPLICATIONS

Jinhai Chen, Qingying Sun

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Abstract

Under the hypothesis that the derivative satisfies some kind of weak Lipschitz condition, sharp estimates of the radii of convergence balls of Newton-like methods for operator equations are given in Banach space. New results can be used to analyze the convergence of other developed Newton iterative methods.

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Under the hypothesis that the derivative satisfies some kind of weak Lipschitz condition, sharp estimates of the radii of convergence balls of Newton-like methods for operator equations are given in Banach space. New results can be used to analyze the convergence of other developed Newton iterative methods.

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Available abstract

Under the hypothesis that the derivative satisfies some kind of weak Lipschitz condition, sharp estimates of the radii of convergence balls of Newton-like methods for operator equations are given in Banach space. New results can be used to analyze the convergence of other developed Newton iterative methods.

Key concepts: Mathematics, Banach space, Lipschitz continuity, Ball (mathematics), Fréchet derivative, Newton's method, Unconditional convergence, Convergence (economics)

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