求解复对称线性系统的改进EPGS迭代法
Improved EPGS Iterative Method for Solving Complex Symmetric Linear Systems
摘要: 本文主要讨论求解复对称线性系统的EPGS迭代法。基于矩阵块三角分裂思想，我们对该方法引入一个加速参数后，得到了改进EPGS迭代法(IEPGS)。我们对IEPGS迭代法进行收敛性分析，给出了收敛性条件，并得到了最优迭代参数及相应的最优收敛因子。数值实验的结果进一步表明了该方法的有效性。
Abstract: In this paper, we mainly discuss the EPGS iterative method for solving complex symmetric linear systems. Based on the idea of triangular splitting of matrix blocks, we introduce an acceleration parameter to this method and obtain the improved EPGS iterative method (IEPGS). We analyze the convergence of IEPGS iteration method, give the condition of convergence, and obtain the optimal iteration parameters and the corresponding optimal convergence factors. Numerical experiments show that the method is effective.
文章引用：隆雪琴, 张乃敏. 求解复对称线性系统的改进EPGS迭代法[J]. 应用数学进展, 2021, 10(11): 3623-3631. https://doi.org/10.12677/AAM.2021.1011383

参考文献

[1] Arridge, S.R. (1999) Optical Tomography in Medical Imaging. Inverse Problems, 15, 41-93. [Google Scholar] [CrossRef] 
[2] Feriani, A., Perotti, F. and Simoncini, V. (2000) Iterative System Solvers for the Frequency Analysis of Linear Mechanical Systems. Computer Methods in Applied Mechanics and Engineering, 190, 1719-1739. [Google Scholar] [CrossRef] 
[3] Howle, V.E., and Vavasis, S.A. (2005) An Iterative Method for Solving Complex-Symmetric Systems Arising in Electrical Power Modeling. SIAM Journal on Matrix Analysis and Applications, 26, 1150-1178. [Google Scholar] [CrossRef] 
[4] Poirier, B.(2000) Efficient Preconditioning Scheme for Block Partitioned Matrices with Structured Sparsity. Numerical Linear Algebra with Applications, 7, 715-726. [Google Scholar] [CrossRef] 
[5] Li, X.A. and Lu, J. (2020) An Equidistant Parameterized Gauss-Seidel Iteration Method for a Class of Block Two-by-Two Linear Systems. Computational and Applied Mathematics, 39, 292. [Google Scholar] [CrossRef] 
[6] Li, X.A., Zhang, W.H. and Wu, Y.J. (2018) On Symmetric Block Triangular Splitting Iteration Method for a Class of Complex Symmetric System of Linear Equations. Applied Mathematics Letters, 79, 131-137. [Google Scholar] [CrossRef] 
[7] Salkuyeh, D.K., Hezari, D. and Edalatpour, V. (2014) Generalized SOR Iterative Method for a Class of Complex Symmetric Linear System of Equations. International Journal of Computer Mathematics, 92, 802-815. [Google Scholar] [CrossRef] 
[8] Bai, Z.Z., Benzi, M. and Chen, F. (2010) Modified HSS Iteration Methods for a Class of Complex Symmetric Linear Systems. Computing, 87, 93-111. [Google Scholar] [CrossRef] 
[9] Li, C.L. and Ma, C.F. (2018) On Euler-Extrapolated Hermitian/Skew-Hermitian Splitting Method for Complex Symmetric Linear Systems. Applied Mathematics Letters, 86, 42-48. [Google Scholar] [CrossRef] 

为你推荐