论文标题
基于矩阵拆分的不适合线性系统的正则迭代方法
Regularized Iterative Method for Ill-posed Linear Systems Based on Matrix Splitting
论文作者
论文摘要
在本文中，引入了矩阵分裂的概念，以通过Tikhonov的正则化解决大型稀疏的不良线性系统。在正规化过程中，我们将不适当的系统转换为适当的系统。通过使用不同类型的矩阵分割来讨论这种良好系统的收敛性。通过操作某些类型的弱分组来研究两个系统的比较分析。此外，我们已经将[Song J和Song Y，Calcolo 48（3），245-260，2011]的双重分裂扩展到了非词II型对非对称矩阵的双重分裂。除此之外，还借助I型和II型的这种弱的双重分裂给出了更多的比较结果。
In this paper, the concept of matrix splitting is introduced to solve a large sparse ill-posed linear system via Tikhonov's regularization. In the regularization process, we convert the ill-posed system to a well-posed system. The convergence of such a well-posed system is discussed by using different types of matrix splittings. Comparison analysis of both systems are studied by operating certain types of weak splittings. Further, we have extended the double splitting of [Song J and Song Y, Calcolo 48(3), 245-260, 2011] to double weak splitting of type II for nonsingular symmetric matrices. In addition to that, some more comparison results are presented with the help of such weak double splittings of type I and type II.
