求解非埃尔米特正定方程组的广义LHSS迭代法

Generalized LHSS method for non-Hermitian positive definite linear systems

基于矩阵的埃尔米特和反埃尔米特分解,李良等给出了一类求解非埃尔米特正定方程组的LHSS迭代法,在系数矩阵的埃尔米特和非埃尔米特之间进行了非对称迭代,在较松弛的约束条件下即可获得收敛结果.本文对该方法做进一步研究,给出了一类求解非埃尔米特正定方程组的广义LHSS迭代方法.数值结果表明,系数矩阵经恰当分解,在处理某些问题时广义LHSS迭代法优于HSS迭代法.

Based on the Hermitian and skew-Hermitian splitting,LI et al proposed a lopsided HSS iteration method for solving non-Hermitian positive definite linear systems which conducts an asymmetric iteration between Hermitian part and skew-Hermitian part.The authors proved that LHSS method converges to the unique solution with a loose constriction of the parameter.To further study LHSS method,a generalized LHSS method is proposed here,which implements an asymmetric iteration between two positive definite parts of the non-Hermitian positive definite coefficient matrix.Theoretical analysis shows that this method converges to the unique solution of the non-Hermitian positive definite linear systems when the parameter satisfies some requirement dominated by the positive definite parts.Experiments show that compared with suitable splitting of coefficient matrix,the generalized LHSS method has better performance than HSS method when dealing with certain linear systems.