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• W2072669068 abstract "The fixed-point iteration algorithm is turned into a quadratically convergent scheme for a system of nonlinear equations. Most of the usual methods for obtaining the roots of a system of nonlinear equations rely on expanding the equation system about the roots in a Taylor series, and neglecting the higher order terms. Rearrangement of the resulting truncated system then results in the usual Newton-Raphson and Halley type approximations. In this paper the introduction of unit root functions avoids the direct expansion of the nonlinear system about the root, and relies, instead, on approximations which enable the unit root functions to considerably widen the radius of convergence of the iteration method. Methods for obtaining higher order rates of convergence and larger radii of convergence are discussed." @default.
• W2072669068 created "2016-06-24" @default.
• W2072669068 creator A5007051207 @default.
• W2072669068 creator A5091768196 @default.
• W2072669068 date "2012-04-05" @default.
• W2072669068 modified "2023-09-23" @default.
• W2072669068 title "A Fixed-Point Iteration Method With Quadratic Convergence" @default.
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• W2072669068 doi "https://doi.org/10.1115/1.4005878" @default.
• W2072669068 hasPublicationYear "2012" @default.
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