scholarly journals Block Preconditioners for Complex Symmetric Linear System with Two-by-Two Block Form

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Shi-Liang Wu ◽  
Cui-Xia Li
Keyword(s):  
Linear System ◽  
Spectral Properties ◽  
Numerical Experiments ◽  
Complex Symmetric Linear Systems ◽  
Block Form ◽  
Complex Symmetric Linear System ◽  
Splitting Iteration Method ◽  
Complex Symmetric ◽  
Block Preconditioners ◽  
Appl Math

Based on the previous work by Zhang and Zheng (A parameterized splitting iteration method for complex symmetric linear systems, Japan J. Indust. Appl. Math., 31 (2014) 265–278), three block preconditioners for complex symmetric linear system with two-by-two block form are presented. Spectral properties of the preconditioned matrices are discussed in detail. It is shown that all the eigenvalues of the preconditioned matrices are well-clustered. Numerical experiments are reported to illustrate the efficiency of the proposed preconditioners.

Accelerated GPMHSS Method for Solving Complex Systems of Linear Equations

2017 ◽  
Vol 7 (1) ◽  
pp. 143-155 ◽  
Author(s):  
Jing Wang ◽  
Xue-Ping Guo ◽  
Hong-Xiu Zhong
Keyword(s):  
Complex Systems ◽  
Linear Systems ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Linear Equations ◽  
Splitting Method ◽  
Complex Symmetric Linear Systems ◽  
Systems Of Linear Equations ◽  
Complex Symmetric ◽  
Symmetric Systems

AbstractPreconditioned modified Hermitian and skew-Hermitian splitting method (PMHSS) is an unconditionally convergent iteration method for solving large sparse complex symmetric systems of linear equations, and uses one parameter α. Adding another parameter β, the generalized PMHSS method (GPMHSS) is essentially a twoparameter iteration method. In order to accelerate the GPMHSS method, using an unexpected way, we propose an accelerated GPMHSS method (AGPMHSS) for large complex symmetric linear systems. Numerical experiments show the numerical behavior of our new method.

scholarly journals A Breakdown-Free Block COCG Method for Complex Symmetric Linear Systems with Multiple Right-Hand Sides

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1302
Author(s):  
Hong-Xiu Zhong ◽  
Xian-Ming Gu ◽  
Shao-Liang Zhang
Keyword(s):  
Linear Systems ◽  
Spectral Properties ◽  
Coefficient Matrix ◽  
Complex Symmetric Linear Systems ◽  
Right Hand ◽  
Orthogonality Conditions ◽  
Free Block ◽  
Complex Symmetric ◽  
The Right ◽  
Conjugate Residual

The block conjugate orthogonal conjugate gradient method (BCOCG) is recognized as a common method to solve complex symmetric linear systems with multiple right-hand sides. However, breakdown always occurs if the right-hand sides are rank deficient. In this paper, based on the orthogonality conditions, we present a breakdown-free BCOCG algorithm with new parameter matrices to handle rank deficiency. To improve the spectral properties of coefficient matrix A, a precondition version of the breakdown-free BCOCG is proposed in detail. We also give the relative algorithms for the block conjugate A-orthogonal conjugate residual method. Numerical results illustrate that when breakdown occurs, the breakdown-free algorithms yield faster convergence than the non-breakdown-free algorithms.

scholarly journals Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Cui-Xia Li ◽  
Yan-Jun Liang ◽  
Shi-Liang Wu
Keyword(s):  
Theoretical Analysis ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Point Of View ◽  
Subspace Methods ◽  
Practical Point ◽  
Complex Symmetric Linear Systems ◽  
Complex Symmetric

Based on the modified Hermitian and skew-Hermitian splitting (MHSS) and preconditioned MHSS (PMHSS) methods, a generalized preconditioned MHSS (GPMHSS) method for a class of complex symmetric linear systems is presented. Theoretical analysis gives an upper bound for the spectral radius of the iteration matrix. From a practical point of view, we have analyzed and implemented inexact GPMHSS (IGPMHSS) iteration, which employs Krylov subspace methods as its inner processes. Numerical experiments are reported to confirm the efficiency of the proposed methods.

A relaxed splitting preconditioner for saddle point problems

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Cui-Xia Li ◽  
Shi-Liang Wu ◽  
Ai-Qun Huang
Keyword(s):  
Saddle Point ◽  
Spectral Properties ◽  
Numerical Experiments ◽  
Saddle Point Problems ◽  
Preconditioned Matrix ◽  
Appl Math

AbstractIn this paper, we introduce a relaxed splitting preconditioner for saddle point problems. Spectral properties of the preconditioned matrix are analyzed and compared with the closely related preconditioner in recent paper [New preconditioners for saddle point problems, Appl. Math. Comput. 172 (2006), 762-771] by Pan et al. Numerical experiments are given to illustrate the efficiency of the proposed precoditioner.

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