求解广义鞍点问题的一个双参数维数分裂方法

Bi-parameterized dimension splitting method for generalized saddle point problem

针对一类广义鞍点问题,利用HSS迭代方法的思想,将单参数维数分裂方法推广到双参数形式。先得到双参数维数分裂迭代法的迭代格式并得到相应的求解广义鞍点问题的双参数DS分裂迭代法,然后证明了该迭代方法是收敛的,改进和推广了求解广义鞍点问题的单参数维数分裂迭代算法。数值实验也验证了双参数DS分裂迭代法比单参数MDS分裂迭代法有效。

By using the idea of HSS iteration method, the single-parameter dimension splitting method of pre- conditioner was generalized to a two-parameter form. The two-parameter dimension splitting form were get and then the two-parameter DS method was used for solve the generalized saddle point problem. Moreover, the new method has been proved to be convergent unconditionally. Numerical experiments showed that the two-parameter DS method was robust and attractive than single-parameter dimension splitting method MDS.