We consider the generalized successive overrelaxation (GSOR) method for solving a class of block three-by-three saddle-point problems. Based on the necessary and sufficient conditions for all roots of a real cubic polynomial to have modulus less than one, we derive convergence results under reasonable assumptions. We also analyze a class of block lower triangular preconditioners induced from GSOR and derive explicit and sharp spectral bounds for the preconditioned matrices. We report numerical experiments on test problems from the liquid crystal director model and the coupled Stokes-Darcy flow, demonstrating the usefulness of GSOR.

翻译：我们考虑了解决一组三、三、三马鞍问题的一系列连续普遍过宽(GSOR)方法;根据真正单立方形的根部低于一个模量的所有必要和充分条件,我们根据合理的假设得出趋同结果;我们还分析一组从GSOR引出的低方形板状三角前置先质,并为先决条件矩阵得出清晰而尖锐的光谱界限;我们报告了液晶导体模型和相伴的斯托克斯-达西流的试验问题数字实验,显示了GSOR的有用性。