Spectral residual methods are derivative-free and low-cost per iteration procedures for solving nonlinear systems of equations. They are generally coupled with a nonmonotone linesearch strategy and compare well with Newton-based methods for large nonlinear systems and sequences of nonlinear systems. The residual vector is used as the search direction and choosing the steplength has a crucial impact on the performance. In this work we address both theoretically and experimentally the steplength selection and provide results on a real application such as a rolling contact problem.

翻译：光谱残存方法是无衍生物的,且每个迭代程序成本低,用于解决非线性方程系统,通常与非线性线性线性搜索战略相配合,并与基于牛顿的大型非线性系统和非线性系统序列方法进行良好比较。残余矢量用作搜索方向,选择阶梯长度对性能有重大影响。在这项工作中,我们从理论上和实验上处理台阶长度的选择,并在诸如滚动接触问题等实际应用上提供结果。