应用数学与计算数学学报
應用數學與計算數學學報
응용수학여계산수학학보
COMMUNICATION ON APPLIED MATHEMATICS AND COMPUTATION
2012年
4期
437-448
,共12页
线性方程组%预处理子%广义极小残量法%谱分析%最小多项式
線性方程組%預處理子%廣義極小殘量法%譜分析%最小多項式
선성방정조%예처리자%엄의겁소잔량법%보분석%최소다항식
systems of linear equations%preconditioner%generalized minimalresidual (GMRES) method%spectrum%minimal polynomial
针对一类具结构的非对称线性方程组提出了一类子结构预处理子, 该预处理子只保留了约束条件的一半项. 研究表明, 预处理矩阵只有三个离散的特征值. 为了避免计算Schur补的逆, 还给出了正则化的子结构预处理子, 同样对预处理矩阵进行了谱分析. 这些结果将Zhou和Niu （Zhou J T, Niu Q. Substructure preconditioners for a class of structured linear systems of equations. Math. Comput. Model., 2010, 52： 1547-1553）的结果推广到非对称结构线性方程组. 数值算例验证了提出的子结构预处理子的有效性.
針對一類具結構的非對稱線性方程組提齣瞭一類子結構預處理子, 該預處理子隻保留瞭約束條件的一半項. 研究錶明, 預處理矩陣隻有三箇離散的特徵值. 為瞭避免計算Schur補的逆, 還給齣瞭正則化的子結構預處理子, 同樣對預處理矩陣進行瞭譜分析. 這些結果將Zhou和Niu （Zhou J T, Niu Q. Substructure preconditioners for a class of structured linear systems of equations. Math. Comput. Model., 2010, 52： 1547-1553）的結果推廣到非對稱結構線性方程組. 數值算例驗證瞭提齣的子結構預處理子的有效性.
침대일류구결구적비대칭선성방정조제출료일류자결구예처리자, 해예처리자지보류료약속조건적일반항. 연구표명, 예처리구진지유삼개리산적특정치. 위료피면계산Schur보적역, 환급출료정칙화적자결구예처리자, 동양대예처리구진진행료보분석. 저사결과장Zhou화Niu （Zhou J T, Niu Q. Substructure preconditioners for a class of structured linear systems of equations. Math. Comput. Model., 2010, 52： 1547-1553）적결과추엄도비대칭결구선성방정조. 수치산례험증료제출적자결구예처리자적유효성.
A substructured preconditioner is proposed for a class of nonsymmetric structured linear systems of equations. This preconditioner keeps only half of the constraint terms. Spectral analysis shows that the preconditioned matrix has only three distinct eigenvalues. To avoid computing the Schur complement, a regularized variant is considered. The spectrum is also analyzed. These theoretical results extend the previous ones (Zhou J T, Niu Q. Substructure preconditioners for a class of structured linear systems of equations. Math. Comput. Model., 2010, 52: 1547-1553). Some numerical examples are presented to show the effectiveness of the proposed preconditioners.
