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，我们写出了抽象非对称区域分解方法的条件数估计。特别地，我们考虑了泊松方程的限制性加法方法，并给出了预处理算子条件数的一个界。我们还得到了预处理算子的非负性。条件数估计对于GMRES等迭代方法的收敛性并不充分，但这些界可能有助于进一步理解非对称区域分解方法。