Field-of-values analysis of preconditioned iterative methods for nonsymmetric elliptic problems
Field-of-values analysis of preconditioned iterative methods for nonsymmetric elliptic problems
复制标题
非对称椭圆问题预处理迭代方法的值域分析
DOI：
10.1007/s002110050306
复制
发表时间：
1997
影响因子：
2.1
通讯作者：
G. Starke
中科院分区：
文献类型：
--
作者：
G. Starke
总结。研究了求解非对称线性方程组的Krylov子空间方法的收敛速度。给出了基于系数矩阵及其逆的值域的最小实部的收敛速度的界。这些数量的估计值可以在迭代过程中从基础的Arnoldi过程中获得。这些边界可用于研究非对称椭圆型边值问题有限元离散预条件的收敛性质，特别是对网格大小和斜对称部分大小的依赖关系。对于构成这类问题的流行的预条件策略的分层基和多级预条件，这一点得到了说明。
Summary. The convergence rate of Krylov subspace methods for the solution of nonsymmetric systems of linear equations, such as GMRES or FOM, is studied. Bounds on the convergence rate are presented which are based on the smallest real part of the field of values of the coefficient matrix and of its inverse. Estimates for these quantities are available during the iteration from the underlying Arnoldi process. It is shown how these bounds can be used to study the convergence properties, in particular, the dependence on the mesh-size and on the size of the skew-symmetric part, for preconditioners for finite element discretizations of nonsymmetric elliptic boundary value problems. This is illustrated for the hierarchical basis and multilevel preconditioners which constitute popular preconditioning strategies for such problems.