scholarly journals A Double-Parameter GPMHSS Method for a Class of Complex Symmetric Linear Systems from Helmholtz Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Cui-Xia Li ◽  
Shi-Liang Wu
Keyword(s):  
Helmholtz Equation ◽  
Linear Systems ◽  
Krylov Subspace ◽  
Krylov Subspace Methods ◽  
Point Of View ◽  
Subspace Methods ◽  
Parameter Region ◽  
Practical Point ◽  
Complex Symmetric Linear Systems ◽  
Complex Symmetric

Based on the preconditioned MHSS (PMHSS) and generalized PMHSS (GPMHSS) methods, a double-parameter GPMHSS (DGPMHSS) method for solving a class of complex symmetric linear systems from Helmholtz equation is presented. A parameter region of the convergence for DGPMHSS method is provided. From practical point of view, we have analyzed and implemented inexact DGPMHSS (IDGPMHSS) iteration, which employs Krylov subspace methods as its inner processes. Numerical examples are reported to confirm the efficiency of the proposed methods.

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.

Iterative solution of linear systems

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 57-100 ◽  
Author(s):  
Roland W. Freund ◽  
Gene H. Golub ◽  
Noël M. Nachtigal
Keyword(s):  
Linear Systems ◽  
Iterative Methods ◽  
Conjugate Gradient ◽  
Krylov Subspace ◽  
Iterative Solution ◽  
Krylov Subspace Methods ◽  
Subspace Methods ◽  
Recent Advances ◽  
Gradient Type ◽  
Large Linear Systems

Recent advances in the field of iterative methods for solving large linear systems are reviewed. The main focus is on developments in the area of conjugate gradient-type algorithms and Krylov subspace methods for nonHermitian matrices.

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