论文标题
延续牛顿的方法，具有非线性方程的残留信任区域时间步长方案
Continuation Newton methods with the residual trust-region time-stepping scheme for nonlinear equations
论文作者
论文摘要
对于非线性方程式，同型方法（持续方法）在工程领域很受欢迎，因为它们的收敛区域很大，并且非常可靠地找到解决方案。经典同质法的缺点是它们的计算时间很重，因为它们需要在中间延续过程中解决许多辅助非线性系统。为了克服这一缺点，我们考虑了针对此问题的剩余信任区域稳定方案的特殊显式延续方法。根据我们的数值实验，与传统优化方法（MATLAB环境的内置subroutine fsolve.m）和同型持续方法（Hompack90和Naclab）相比，新方法更强大，更快地找到现实世界问题所需的解决方案。此外，我们分析了新方法的全局收敛性和局部超级线性收敛性。
For nonlinear equations, the homotopy methods (continuation methods) are popular in engineering fields since their convergence regions are large and they are quite reliable to find a solution. The disadvantage of the classical homotopy methods is that their computational time is heavy since they need to solve many auxiliary nonlinear systems during the intermediate continuation processes. In order to overcome this shortcoming, we consider the special explicit continuation Newton method with the residual trust-region time-stepping scheme for this problem. According to our numerical experiments, the new method is more robust and faster to find the required solution of the real-world problem than the traditional optimization method (the built-in subroutine fsolve.m of the MATLAB environment) and the homotopy continuation methods(HOMPACK90 and NAClab). Furthermore, we analyze the global convergence and the local superlinear convergence of the new method.
