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2014•Journal of Applied MathematicsOpen access

Convergence Theorem for a Family of New Modified Halley’s Method in Banach Space

Rongfei Lin, Yueqing Zhao, Qingbiao Wu, Jueliang Hu

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Abstract

We establish convergence theorems of Newton-Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate. To show the application of our theorems, two numerical examples are given.

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What this paper is about

We establish convergence theorems of Newton-Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate. To show the application of our theorems, two numerical examples are given.

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Available abstract

We establish convergence theorems of Newton-Kantorovich type for a family of new modified Halley’s method in Banach space to solve nonlinear operator equations. We present the corresponding error estimate. To show the application of our theorems, two numerical examples are given.

Key concepts: Banach space, Mathematics, Convergence (economics), Unconditional convergence, Applied mathematics, Nonlinear system, Operator (biology), Space (punctuation)

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