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| 1 | HSS METHOD WITH A COMPLEX PARAMETER FOR THE SOLUTION OF COMPLEX LINEAR SYSTEM显示文摘在这份报纸,一个复杂参数在切开的 Hermitian 和 skew-Hermitian (HSS ) 被采用方法(黄雾, Golub 和 Ng:暹罗 J。矩阵肛门。Appl, 24 (2003 ) , 603-626 ) 为解决复杂线性系统斧子 = f。当时,产生方法的集中被证明矩阵的光谱在权利的一个谎言上面(或更低) 复杂飞机的部分。我们也导出上面的界限光谱 HSS 重复矩阵的半径,和一个估计的最佳的参数(表示了由[est ]) 这,上面的界限被介绍。二个修改模型问题的数字实验证明 HSS 方法与[est ] 一更小光谱半径比那与最小化相应上面的界限的真实参数。特别地为矩阵 A 的“主导”的想象的部分,这改进是可观的。我们也与我们的参数由 HSS preconditioning 矩阵测试 GMRES 方法 preconditioned [est ] 。[从作者抽象] | Guiding Gu | 2011 | Journal of Computational Mathematics2011，29，4： | 2 |
| 2 | IMPROVED PMHSS ITERATION METHODS FOR COMPLEX SYMMETRIC LINEAR SYSTEMS显示文摘Based on the preconditioned modified Hermitian and skew-Hermitian splitting (PMHSS) iteration method for the complex symmetrie linear system, two improved iterative methods, namely, the modified PMHSS (MPMHSS) method and the double modified PMHSS (DMPMHSS) method, are proposed in this paper. The spectra] radii of the iteration matrices of two methods are given. We show that by choosing an appropriate parameter, MPMHSS could speed up the convergence on PMHSS. The DMPMHSS method is a four-step alternating iteration that is developed upon the two-step alternating iteration of MPMHSS. We discuss the choice of the parameters and establish the convergence of DMPMHSS. In particular, we give an analysis of the spectral radius of PMHSS and DMPMHSS at the parameter free situation, and we show that DMPMHSS converges faster than PMHSS in most cases. Our numerical experiments show these points. | Kai Liu Guiding Gu | 2019 | Journal of Computational Mathematics2019，37，2： | 1 |
| 3 | A block EN algorithm for non- symmetric linear systems with eigenvectors 显示文摘 | Gu Guiding Wu Hebing | 2001 | Applied Mathematics and Computation2001，121，： | 1 |
| 4 | Restarted FOM Augmented with Ritz Vectors for Shifted Linear Systems显示文摘The restarted FOM method presented by Simoncini[7]according to the natural collinearity of all residuals is an efficient method for solving shifted systems,which generates the same Krylov subspace when the shifts are handled simultaneously.However,restarting slows down the convergence.We present a practical method for solving the shifted systems by adding some Ritz vectors into the Krylov subspace to form an augmented Krylov subspace. Numerical experiments illustrate that the augmented FOM approach(restarted version)can converge more quickly than the restarted FOM method. | Zhanwen Li Guiding Gu | 2006 | Numerical Mathematics A Journal of Chinese Universities(English Series)2006，15，1： | 1 |
| 5 | GENERAL FULL IMPLICIT STRONG TAYLOR APPROXIMATIONS FOR STIFF STOCHASTIC DIFFERENTIAL EQUATIONS显示文摘In this paper,we present the backward stochastic Taylor expansions for a Ito process,including backward Ito-Taylor expansions and backward Stratonovich-Taylor expansions.We construct the general full implicit strong Taylor approximations(including Ito-Taylor and Stratonovich-Taylor schemes)with implicitness in both the deterministic and the stochastic terms for the stiff stochastic differential equations(SSDE)by employing truncations of backward stochastic Taylor expansions.We demonstrate that these schemes will converge strongly with corresponding order 1,2,3,....Mean-square stability has been investigated for full implicit strong Stratonovich-Taylor scheme with order 2,and it has larger meansquare stability region than the explicit and the semi-implicit strong Stratonovich-Taylor schemes with order 2.We can improve the stability of simulations considerably without too much additional computational effort by using our full implicit schemes.The full implicit strong Taylor schemes allow a larger range of time step sizes than other schemes and are suitable for SSDE with stiffness on both the drift and the diffusion terms.Our numerical experiment show these points. | Kai Liu Guiding Gu | 2022 | Journal of Computational Mathematics2022，40，4： | 0 |
| 6 | ON CONVERGENCE PROPERTY OF THE LANCZOS METHOD FOR SOLVING A COMPLEX SHIFTED HERMITIAN LINEAR SYSTEM显示文摘我们为解决一个复杂转移 Hermitian 线性系统(伪 I + H ) 讨论 Lanczos 方法的集中性质 x = f。由显示出二个系统的剩余的 colinear 系数,我们的集中分析在条件 Re 下面揭示那(在(H) 的伪)+位 m > 0,方法为真实转移 Hermitian 线性系统比那快收敛(Re (伪) 我 + H ) x = f。数字实验验证如此的集中性质。[从作者抽象] | Guiding Gu | 2013 | Journal of Computational Mathematics2013，31，3： | 0 |
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