The classical Newton iterative method is a way for solving nonlinear equations in the real and complex domains by approxima-ting the roots of nonlinear equations,which can be realized by deriving the integration functions on variable lines.The four integral func-tions are obtained by approximating the area of curved-edge trapezoid,and the improved Newton's iterative method for solving the ap-proximate roots of nonlinear equations with fifth-order convergence is obtained by the gradient-weighted reconstruction assignment.The convergence analysis and numerical examples verify that this method has a fast convergence rate and can effectively avoid divergence near multiple roots.It has a very wide range of applications in the field of nonlinear engineering,economics and artificial intelligence.
关键词
加权/五阶收敛/非线性方程/改进牛顿迭代
Key words
weighted/fifth-order convergence/nonlinear equationin/improved Newton iteration
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