兰州大学学报（自然科学版）
蘭州大學學報（自然科學版）
란주대학학보（자연과학판）
JOURNAL OF LANZHOU UNIVERSITY（NATURAL SCIENCES）
2014年
6期
881-888
,共8页
不对称HSS分裂%预处理%最优参数%Sylvester方程组
不對稱HSS分裂%預處理%最優參數%Sylvester方程組
불대칭HSS분렬%예처리%최우삼수%Sylvester방정조
asymmetric HSS%preconditioning%optimal parameter%Sylvester equation
针对系数矩阵为大型非Hermitian正定/半正定稀疏矩阵的连续Sylvester方程组，提出了预处理不对称的埃尔米特和反埃尔米特分裂(PAHSS)迭代方法，并对所提算法进行了收敛性分析，讨论了PAHSS方法的准最优参数。为了进一步减少计算量，在内迭代求解子线性方程组时，基于该子线性系统具有特殊结构，采用某种有效的迭代方法去求解，得到了不精确的PAHSS迭代方法，并分析了其收敛性。数值实验验证了所提算法的有效性。
針對繫數矩陣為大型非Hermitian正定/半正定稀疏矩陣的連續Sylvester方程組，提齣瞭預處理不對稱的埃爾米特和反埃爾米特分裂(PAHSS)迭代方法，併對所提算法進行瞭收斂性分析，討論瞭PAHSS方法的準最優參數。為瞭進一步減少計算量，在內迭代求解子線性方程組時，基于該子線性繫統具有特殊結構，採用某種有效的迭代方法去求解，得到瞭不精確的PAHSS迭代方法，併分析瞭其收斂性。數值實驗驗證瞭所提算法的有效性。
침대계수구진위대형비Hermitian정정/반정정희소구진적련속Sylvester방정조，제출료예처리불대칭적애이미특화반애이미특분렬(PAHSS)질대방법，병대소제산법진행료수렴성분석，토론료PAHSS방법적준최우삼수。위료진일보감소계산량，재내질대구해자선성방정조시，기우해자선성계통구유특수결구，채용모충유효적질대방법거구해，득도료불정학적PAHSS질대방법，병분석료기수렴성。수치실험험증료소제산법적유효성。
A preconditioned asymmetric Hermitian and skew-Hermitian splitting (PAHSS) method was present-ed for solving large sparse continuous Sylvester equations with non-Hermitian and positive definite/semi-definite matrices. The convergent property of the PAHSS method was also discussed. The choice of the quasi-optimal parameter of the PAHSS method was studied. To further reduce the computing cost, an inexact preconditioned asymmetric HSS splitting (IPAHSS) iteration method was used, together with a certain e?cient iterative method to approximately solve the two specially preconditioned structured continuous Sylvester equations involved in each step of the AHSS iteration. The convergence of the IPAHSS iteration method was also studied in detail. Numerical experiments demonstrated the e?ciency of the PAHSS method with different choices of the parame-ters for the continuous Sylvester equations.
