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A weak condition for secant method to solve systems of nonlinear equations. (English) Zbl 1199.65170

Summary: A new weak condition for the convergence of the secant method when solving systems of nonlinear equations is proposed. The convergence ball with center \(x_0\) is replaced by that of \(x_1\), 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 the 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.

MSC:

65H10 Numerical computation of solutions to systems of equations
65Y20 Complexity and performance of numerical algorithms
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