|
|
- 2016
基于超松弛迭代的MHSS加速方法
|
Abstract:
摘要： 修正的Hermite/反Hermite分裂(MHSS)迭代方法是一类求解大型稀疏复对称线性代数方程组的无条件收敛的迭代算法。基于超松弛(SOR)迭代技术,本文提出一类MHSS加速方法,分析了MHSS加速方法的收敛性质,给出了MHSS加速方法中参数ω的选取办法。数值实验证明了新方法能够有效地提高MHSS求解线性代数方程组的求解效率。
Abstract: Modified Hermitian and skew-Hermitian splitting(MHSS)iteration method is an unconditionally convergent method for solving large sparse complex symmetric linear systems. Based on successive-overrelaxation technique, a class of accelerated MHSS iterative method is presented, then convergence theorems is established for the new method. Moreover, a selection method of the parameter ω is given. Numerical experiment demonstrate that new method can effectively improve the efficiency of MHSS iterative method for solving linear algebraic equations
| [1] | ARRIDGE H R. Optical tomography in medical imaging[J]. Inverse Problem, 1999, 15:R41-R93. |
| [2] | VAN DIJK W, TOYAMA F M. Accurate numerical solutions of the time-dependent Schrodinger equation[J]. Physical Review E, 2007, 75:036707-1-036707-10. |
| [3] | POIRIER B. Efficient preconditioning scheme for block partitioned matrices with structured sparsity[J]. Numerical Linear Algebra with Applications, 2000, 7:715-726. |
| [4] | FERIANI A, PEROTTI F, SIMONCINI V. Iterative system solvers for the frequency Analysis of linear mechanical systems[J]. Computer Methods in Applied Mechanics and Engineering, 2000, 190:1719-1739. |
| [5] | BENZI M, BERTACCINI D. Block preconditioning of real-valued iterative algorithms for complex linear systems[J]. IMA Journal of Numerical Analysis, 2008, 28:598-618. |
| [6] | 王洋,付军,马维元.非埃尔米特正定线性系统的预条件NSS方法[J].山东大学学报(理学版),2012,47(6):57-62. WANG Yang, FU Jun, MA Weiyuan. Preconditioned NSS methods for non-Hermitian and positive definite linear systems[J]. Journal of Shandong University(Natural Science), 2012, 47(6):57-62. |
| [7] | BAI Zhongzhi, GOLUB G H, MICHAEL K Ng. Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems[J]. SIAM J Matrix Analysis with Applications, 2003, 24(3):603-626. |
| [8] | BAI Zhongzhi, GOLUB G H, MICHAEL K Ng. On successive overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations[J]. Numerical Linear Algebra with Applications, 2007, 14:319-335. |
| [9] | AXELSSON O, KUCHCROV A. Real valued iterative methods for solving complex symmetric linear systems[J]. Numerical Linear Algebra with Applications, 2000, 7:197-218. |
| [10] | BAI Zhongzhi, BENZI M, CHEN Fang. Modified HSS Iteration Methods for a class of complex symmetric Linear Systems[J]. Computing, 2010, 87(3-4):93-111. |
| [11] | BAI Zhongzhi, BENZI M, CHEN Fang. On preconditioned MHSS iteration methods complex symmetric linear systems[J]. Numerical Algorithms, 2011, 56(2):297-317. |
| [12] | BAI Zhongzhi. On SSOR-like preconditioners for non-Hermitian positive definite matrices[J]. Numerical Linear Algebra with Applications, 2016, 23:37-60. |
| [13] | VARGA R. Matrix iterative analysis[M]. 2nd ed. New York: Springer, 2000. |
| [14] | WANG Yang, WU Yujiang, FAN Xiaoyan. Two-parameter preconditioned NSS method for non-Hermitian and positive definite linear systems[J]. Communication on Applied Mathematics and Computation, 2013, 27(3):322-340. |
| [15] | YOUNG D. Iterative solution of large linear systems[M]. New York: Academic Press, 1971. |
