WANG Maoxiao,LI Shengkun.Complex Global QMR Algorithm for the Complex Matrix Equations[J].Journal of Chengdu University of Information Technology,2020,35(02):246-252.[doi:10.16836/j.cnki.jcuit.2020.02.018]
复矩阵方程的复全局QMR算法
- Title:
- Complex Global QMR Algorithm for the Complex Matrix Equations
- 文章编号:
- 2096-1618(2020)02-0248-05
- 关键词:
- 复矩阵方程; 实内积; 全局M-双正交化过程; 全局QMR算法
- Keywords:
- complex matrix equations; real inner product; global M-biorthogonalization process; global QMR algorithm
- 分类号:
- O241.6
- 文献标志码:
- A
- 摘要:
- 研究复矩阵方程的全局krylov子空间算法。以复矩阵的实内积为工具,提出一种复全局M-双正交化过程。基于该过程,得到一种新的复全局QMR算法求解复矩阵方程。数值算例表明该算法比现有的算法更有效。
- Abstract:
- In this paper, we study the global Krylov subspace algorithm for the complex matrix equations. Using the real inner product of complex matrices, a complex global M-biorthogonalization process is proposed. Based on this process, a new complex global QMR algorithm is obtained to solve the complex matrix equations. The numerical examples show that the algorithm is more effective than the existing methods.
参考文献/References:
[1] L D Liao,G F Zhang.Preconditioning of complex linear systems from the Helmholtz equation[J].Comput.Math.Appl.,2016,72:2473-2485.
[2] D Kressner,C Schr¨oder,D S Watkins.Implicit QR algorithms for palindromic and even eigenvalue problems[J].Numer.Algor.,2009,51:209-238.
[3] J H Bevis,F J Hall,R E Hartwig.The matrix equation AX+(-overX)B=C and its special cases[J].SIAM J.Matrix Anal.Appl.,1988,9:348-359.
[4] V Simoncini,On the numerical solution of AX-XB=C and its special cases[J].SIAM J.Matrix Anal.Appl.,1988,9:348-359.
[4] V Simoncini,On the numerical solution of .BIT,1996,36:814-830.
[5] M Robbe,M Sadkane.A convergence analysis of GMRES and FOM methods for Sylvester equations[J].Numer.Algor.,2002,30:71-89.
[6] A El Guennouni,K Jbilou,A J Riquet. Block Krylov subspace methods for solving large Sylvester equations[J].Numer.Algor.,2002,29:75-96.
[7] K Jbilou.Low rank approximate solutions to large Sylvester matrix equations[J].Appl.Math.Comput.,2006,177:365-376.
[8] L Bao,Y Q Lin,Y M Wei.A new projection method for solving large Sylvester equations[J].Appl.Numer.Math.,2007,57:521-532.
[9] A Bouhamidi K Jbilou.A note on the numerical approximate solutions for generalized Sylvester matrix equations with applications[J].Appl.Math.Comput.,2008,206:687-694.
[10] F P A Beik D K Salkuyeh.On the global Krylov subspace methods for solving general coupled matrix equations[J].Comput.Math.Appl.,2011,62:4605-4613.
[11] F P A Beik.Theoretical results on the global GMRES method for solving generalized Sylvester matrix equations[J].Bull.Iranian Math.Soc.,2014,40:1097-1117.
[12] A Kaabi.On the numerical solution of generalized Sylvester matrix equations[J].Bull.Iranian Math.Soc.,2014,40:101–113.
[13] M Heyouni,F.Saberi-Movahed,A Tajaddini.On global Hessenberg based methods for solving Sylvester matrix equations[J].Comput.Math.Appl.2019,77:77-92.
[14] S K Li T Z Huang.LSQR iterative method for generalized coupled Sylvester matrix equations[J].Appl.Math.Model.,2012,36:3545-3554.
[15] A G Wu,L L Lv,G R Duan.Iterative algorithms for solving a class of complex conjugate and transpose matrix equations[J].Appl. Math.Comput.,2011,217:8343-8353.
[16] A G Wu,G Feng,G R Duan,et al.Finite iterative solutions to a class of complex matrix equations with conjugate and transpose of the unknowns[J].Math.Comput. Model.,2010,52:1463-1478.
[17] L J Zhao,X Y Hu,L Zhang.Linear restriction problem of Hermitian reflexive matrices and its approximation[J].Appl.Math.Comput.,2008,200:341-351.
[18] R Bouyouli,K Jbilou,R.Sadaka,et al.Convergence properties of some block Krylov subspace methods for multiple linear systems[J].J Comput.Appl.Math.,2006,196:498-511.
[19] K Jbilou,H.Sadok,A Tinzefte Oblique projection methods for linear systems with multiple right-hand sides[J].Electron.T.Numer.Ana.,2005,20:119-138.
[20] Y F Jing,T Z Huang,Y Zhang,et al.Lanczos-type variants of the COCR method for complex nonsymmetric linear systems[J].J.Comput.Phys.,2009,228:6376-6394.
[21] B Carpentieri,Y F Jing,T Z Huang.The BiCOR and CORS iterative algorithms for solving nonsymmetric linear systems[J].SIAM J.Sci.Comput.,2011,33:3020-3036.
[22] R W Freund N M Nachtigal.QMR:a quasi-minimal residual method for non-Hermitian linear systems[J].Numer.Math.,1991,60:315-339.
备注/Memo
收稿日期:2019-09-10 基金项目:四川省科技厅应用基础研究资助项目(2019YJ0357); 四川省教育厅重点资助项目(16ZA0220)