Sharp error bounds of some Krylov subspace methods for non-Hermitian linear systems
Sharp error bounds of some Krylov subspace methods for non-Hermitian linear systems
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DOI：
10.1016/s0096-3003(99)00027-2
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发表时间：
2000-03
期刊：
影响因子：
--
通讯作者：
Z. Bai
中科院分区：
文献类型：
--
作者：
Z. Bai
Krylov子空间方法的收敛性，例如，全正交法（FOM）和广义最小残差法（GMRES）等，当系数矩阵为亏损矩阵时，特别是当其谱位于开右（左）半平面或在真实的轴上时，统一而详细地研究了求解大型非Hermite线性方程组的建立了相关的理论误差界，揭示了收敛性与系数矩阵特征值之间的内在联系。这些结果不仅推广了文献中关于可对角化矩阵的所有已知结果，而且改进了贾（数学学报（新辑）14（1998）507-518）中的相应估计.
The convergence of the Krylov subspace methods, e.g., Full Orthogonal Method (FOM) and Generalized Minimal Residual Method (GMRES), etc., for solving large non-Hermitian linear systems is studied in a unified and detailed way when the coefficient matrix is defective; in particular, when its spectrum lies in the open right (left) half plane or is on the real axis. Related theoretical error bounds are established, which reveal some intrinsic relationships between the convergence properties and the eigen-characteristics of the coefficient matrix. These results not only generalize all the known ones for the diagonalizable matrices in the literature, but also sharp the corresponding estimates in Jia (Acta Mathematica Sinica (New Series) 14 (1998) 507–518).