Abstract
In this paper, a new weak condition for the convergence of secant method to solve the systems of nonlinear equations is proposed. A convergence ball with the center x 0 is replaced by that with x 1, the first approximation generated by the secant method with the initial data x −1 and x 0. Under the bounded conditions of the divided difference, a convergence theorem is obtained and two examples to illustrate the weakness of convergence conditions are provided. Moreover, the secant method is applied to a system of nonlinear equations to demonstrate the viability and effectiveness of the results in the paper.
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Supported by the Qianjiang Rencai Project Foundation of Zhejiang Province (J20070288).
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Liang, Kw., Han, Df., Zhang, H. et al. A weak condition for secant method to solve systems of nonlinear equations. Appl. Math. J. Chin. Univ. 24, 90–96 (2009). https://doi.org/10.1007/s11766-009-1975-9
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DOI: https://doi.org/10.1007/s11766-009-1975-9