Global GPBiCGstab(L) method for solving linear matrix equations
Global GPBiCGstab(L) method for solving linear matrix equations
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DOI：
10.1007/s11075-022-01415-7
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发表时间：
2022-11
影响因子：
2.1
通讯作者：
Itsuki Horiuchi;Kensuke Aihara;Toshio Suzuki;E. Ishiwata
中科院分区：
文献类型：
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作者：
Itsuki Horiuchi;Kensuke Aihara;Toshio Suzuki;E. Ishiwata
全局Krylov子空间方法是求解大型线性矩阵方程的有效迭代方法。几种用于求解标准线性方程组的lanczos型积法（ltpm）已经扩展到它们的全局版本。然而，GPBiCGstab(L)方法结合了两种著名的ltpm方法（即BiCGstab(L)和GPBiCG方法），最近得到了发展，并且与传统的ltpm方法相比，这种新方法具有优越的收敛性。因此，在本研究中，我们将GPBiCGstab(L)方法扩展到其全球版本。在这里，我们不仅提出了原始GPBiCGstab(L)算法的朴素扩展，而且提出了它的替代实现。这种变体使预处理技术能够稳定有效地应用。数值实验结果表明，本文提出的全局GPBiCGstab(L)方法是有效的。
Global Krylov subspace methods are effective iterative solvers for large linear matrix equations. Several Lanczos-type product methods (LTPMs) for solving standard linear systems of equations have been extended to their global versions. However, the GPBiCGstab(L) method, which unifies two well-known LTPMs (i.e., BiCGstab(L) and GPBiCG methods), has been developed recently, and it has been shown that this novel method has superior convergence when compared to the conventional LTPMs. In the present study, we therefore extend the GPBiCGstab(L) method to its global version. Herein, we present not only a naive extension of the original GPBiCGstab(L) algorithm but also its alternative implementation. This variant enables the preconditioning technique to be applied stably and efficiently. Numerical experiments were performed, and the results demonstrate the effectiveness of the proposed global GPBiCGstab(L) method.