一个新型自适应预条件的总体CGS算法

A New Adaptive Preconditioned Global CGS Algorithm

总体CGS算法(Gl-CGS)是求解具有多个右端项大型稀疏非对称线性方程组的一个有效矩阵Krylov子空间方法.然而,在一些实际问题中Gl-CGS算法常常收敛得很慢甚至停滞.针对此问题,将总体CGS算法嵌入总体GMRES迭代过程,构造了一个新型自适应预条件子.最后,数值试验表明此预条件子的有效性.

Global CGS algorithm（Gl-CGS） is popular matrix Krylov subspace method for large,sparse and nonsymmetric linear systems with multiple right-hand sides.However,the Gl-CGS may suffer from slow convergence or be stationary in some applications.In order to remedy this,we present a new adaptive preconditioner,which is constructed in the iteration.step of Gl-CGS,by several steps of global GMRES（m）.Finally,numerical experiments show the effectiveness of the new preconditioner.