| 非对称线性方程组的可变预处理GPBi-CG方法 |
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| 引用本文： | 王佳敏,谷同祥.非对称线性方程组的可变预处理GPBi-CG方法[J].聊城大学学报(自然科学版),2012(1):25-29. |
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| 作者姓名： | 王佳敏 谷同祥 |
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| 作者单位： | 中国工程物理研究院研究生部;北京应用物理与计算数学研究所计算物理试验室 |
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| 基金项目： | 国家自然科学基金(61170309,60973151,91130024)资助项目 |
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| 摘 要： | 给出了可变预处理形式的GPBi-CG方法,在算法的每一步中它用不同的预处理子.特别地,可变预处理子的灵活性是可用任何一种迭代法得到.例如,标准的GPBi-CG算法自身可以作为预处理子,其他的Krylov子空间法或是分裂迭代法也可以.对于可变预处理形式的GPBi-CG方法,我们还进行了一些数值试验,包括一些非对称矩阵.这些算例表明了可变预处理迭代法的收敛性和可靠性.
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| 关 键 词： | Krylov子空间法 可变预处理 内外迭代 GPBi-CG |
Flexible GPBi-CG for Nonsymmetric Linear Systems |
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| WANG Jia-min,GU Tong-xiang.Flexible GPBi-CG for Nonsymmetric Linear Systems[J].Journal of Liaocheng University:Natural Science Edition,2012(1):25-29. |
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| Authors: | WANG Jia-min GU Tong-xiang |
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| Institution: | 1.Graduate School of Chinese Academy of Engineering Physics,Mianyang 621900,China;2.Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics,Beijing 100088,China) |
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| Abstract: | We present a flexible version of GPBi-CG algorithm which allows for the use of a different preconditioner at each step of the algorithm.In particular,a result of the flexibility of the variable preconditioner is to use any iterative method.For example,the standard GPBi-CG algorithm itself can be used as a preconditioner,as can other Krylov subspace methods or splitting methods.Numerical experiments are conducted for flexible GPBi-CG for a few matrices including some nonsymmetric matrices.These experiments illustrate the convergence and robustness of the flexible iterative method. |
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| Keywords: | Krylov subspace method flexible preconditioning inner-outer iteration GPBi-CG |
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