In this paper, we propose a new filter algorithm for the system of nonlinear equations. In previous work, the feasibility recovery phase is used to make up for the defect of the filter method, which requires a lot of calculation. To avoid it, the new algorithm is equipped with a new filter. At the same time, we discuss the division of the system of nonlinear equations so that the algorithm can achieve the best numerical results. The new algorithm switches to back tracking steps when a trial step produced by the trust region subproblem is unacceptable. Combining the new filter with both trust region and line search method, the convergence of the algorithm is obtained. The numerical results show the effectiveness of the new algorithm.

中文翻译：

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非线性方程组的一种新的滤波算法

在本文中，我们为非线性方程组提出了一种新的滤波算法。在先前的工作中，可行性恢复阶段用于弥补过滤方法的缺陷，该缺陷需要大量的计算。为了避免这种情况，新算法配备了新的过滤器。同时，我们讨论了非线性方程组的划分，以使算法能够获得最佳数值结果。当由信任区域子问题产生的试验步骤不可接受时，新算法将切换到反向跟踪步骤。将新的滤波器与信赖域和线搜索方法相结合，获得了算法的收敛性。数值结果表明了该算法的有效性。