Preconditioning complex symmetric linear systems
This work provides a practical preconditioning technique for solving complex symmetric linear systems, which are common in scientific computing, but the improvement is incremental over existing methods.
The paper presents a new polynomial preconditioner for complex symmetric linear systems, based on Hermitian and skew-Hermitian splitting, that improves the efficiency and robustness of COCG and COCR solvers without requiring spectral estimates. Numerical results demonstrate its effectiveness.
A new polynomial preconditioner for symmetric complex linear systems based on Hermitian and skew-Hermitian splitting (HSS) for complex symmetric linear systems is herein presented. It applies to Conjugate Orthogonal Conjugate Gradient (COCG) or Conjugate Orthogonal Conjugate Residual (COCR) iterative solvers and does not require any estimation of the spectrum of the coefficient matrix. An upper bound of the condition number of the preconditioned linear system is provided. Moreover, to reduce the computational cost, an inexact variant based on incomplete Cholesky decomposition or orthogonal polynomials is proposed. Numerical results show that the present preconditioner and its inexact variant are efficient and robust solvers for this class of linear systems. A stability analysis of the method completes the description of the preconditioner.