A weighted simpler GMRES algorithm for shifted linear systems
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摘要: 结合加权策略和简化的广义最小残量算法（GMRES），提出可有效求解位移线性方程组的加权简化GMRES算法，并给出加权简化GMRES算法与简化GMRES算法之间的联系与性质，最后数值算例给出了新算法的有效性.Abstract: Combining the strategy of weighted and simpler GMRES methods, this paper presents a weighted simpler GMRES algorithm for solving shifted linear systems, and gives some properties of the proposed algorithm. Numerical results illustrate the performance and effectiveness of the algorithm.
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Key words:
- shifted linear systems /
- simpler GMRES /
- weighted matrix
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表 1 实验所用矩阵信息
Tab. 1 The content of the test matrices
矩阵名称 大小 非零元个数 条件数 应用领域 add20 2 395$\times$2 395 13 151 1.76$\times10^{4}$ 半导体系统设计技术 bfw782a 782$\times$782 7 516 4.6$\times10^{3}$ 电磁学 memplus 17 758$\times$17 758 126 150 2.67$\times10^{5}$ 电路仿真 sherman4 1 104$\times$1 104 3 786 7.16$\times10^{3}$ 计算流体力学 young1c 841$\times$841 4 089 1.01$\times10^{3}$ 声学 CONF6.0-00L4X4-2000 3 072$\times$3 072 119 808 8.35$\times10^{2}$ QCD 
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表 2 SGMRES-Sh与WSGMRES-Sh的数值结果比较
Tab. 2 Comparison of SGMRES-Sh and WSGMRES-Sh
矩阵名称 SGMRES-Sh 加权矩阵 WSGMRES-Sh $cpu$ $mv$ $cpu$ $mv$ add20 0.341 1 199 $D^1$ 0.352 1 531 $D^2$ 0.150 533 bfw782a 0.525 3 779 $D^1$ 0.383 2 837 $D^2$ 0.199 1 395 memplus 11.843 7 921 $D^1$ 10.391 6 077 $D^2$ 3.099 1 819 sherman4 0.130 663 $D^1$ 0.080 447 $D^2$ 0.100 600 young1c 1.330 5 524 $D^1$ 1.109 5 044 $D^2$ 0.989 4 489 $\rm A_{\rm QCD}$ 2.812 2 413 $D^1$ 0.660 509 $D^2$ 0.683 509
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