Using oblique projections and angles between subspaces we write condition number estimates for abstract nonsymmetric domain decomposition methods. In particular, we consider a restricted additive method for the Poisson equation and write a bound for the condition number of the preconditioned operator. We also obtain the non-negativity of the preconditioned operator. Condition number estimates are not enough for the convergence of iterative methods such as GMRES but these bounds may lead to further understanding of nonsymmetric domain decomposition methods.
翻译:利用斜投影和子空间之间的夹角,我们为抽象的非对称域分解方法编写了条件数估计。具体而言,我们考虑了关于Poisson方程的一个限制性加法方法,并编写了预处理算子的条件数上限。我们还获得了预处理算子的非负性。条件数估计并不足以保证迭代方法(如GMRES)的收敛性,但是这些上限可能会带来更深入的理解非对称域分解方法。