Sequential Residual Methods try to solve nonlinear systems of equations $F(x)=0$ by iteratively updating the current approximate solution along a residual-related direction. Therefore, memory requirements are minimal and, consequently, these methods are attractive for solving large-scale nonlinear systems. However, the convergence of these algorithms may be slow in critical cases; therefore, acceleration procedures are welcome. In this paper, we suggest to employ a variation of the Sequential Secant Method in order to accelerate Sequential Residual Methods. The performance of the resulting algorithm is illustrated by applying it to the solution of very large problems coming from the discretization of partial differential equations.

翻译：序列残存方法试图解决非线性方程式的非线性系统 $F(x)=0美元,办法是沿残余相关方向反复更新当前近似解决办法,因此,内存要求微乎其微,因此,这些方法对解决大规模非线性系统具有吸引力,然而,这些算法在关键情况下的趋同速度可能较慢;因此,加速程序是值得欢迎的。在本文件中,我们建议采用序列静态方法的变异,以加速序列残存方法。由此产生的算法的性能通过应用它解决部分差异方程式离散产生的非常大的问题来说明。