非对称线性方程组的可变预处理GPBi-CG方法

Flexible GPBi-CG for Nonsymmetric Linear Systems

给出了可变预处理形式的GPBi-CG方法,在算法的每一步中它用不同的预处理子.特别地,可变预处理子的灵活性是可用任何一种迭代法得到.例如,标准的GPBi-CG算法自身可以作为预处理子,其他的Krylov子空间法或是分裂迭代法也可以.对于可变预处理形式的GPBi-CG方法,我们还进行了一些数值试验,包括一些非对称矩阵.这些算例表明了可变预处理迭代法的收敛性和可靠性.

We present a flexible version of GPBi-CG algorithm which allows for the use of a different preconditioner at each step of the algorithm.In particular,a result of the flexibility of the variable preconditioner is to use any iterative method.For example,the standard GPBi-CG algorithm itself can be used as a preconditioner,as can other Krylov subspace methods or splitting methods.Numerical experiments are conducted for flexible GPBi-CG for a few matrices including some nonsymmetric matrices.These experiments illustrate the convergence and robustness of the flexible iterative method.