论文标题
顺序残留方法的固定加速度求解大型非线性方程式
Secant acceleration of sequential residual methods for solving large-scale nonlinear systems of equations
论文作者
论文摘要
顺序残差方法试图通过沿剩余方向更新当前的近似解决方案来求解方程式$ f（x）= 0 $的非线性系统。因此，内存需求是最小的，因此，这些方法对于解决大规模的非线性系统具有吸引力。但是，在关键情况下，这些算法的收敛可能很慢。因此，欢迎加速程序。在本文中，我们建议采用顺序割方法的变体，以加速顺序残留方法。通过将其应用于偏微分方程离散化的非常大问题的解决方案来说明所得算法的性能。
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.
