大型实对称特征值问题的块Jacobi-Davidson方法的不精确求解  

On the Imprecise Solution to Block Jacobi-Davidson Method for Large Real Symmetric Eigenvalue Problems

作　　者：谭静[1,2] 汪晓红[1] 

机构地区：[1]南京航空航天大学理学院,南京210016 [2]淮安信息职业技术学院基础部,江苏淮安223003

出　　处：《西安文理学院学报（自然科学版）》2012年第4期38-44,共7页Journal of Xi’an University(Natural Science Edition)

摘　　要：块Jacobi-Davidson方法是计算大型实对称矩阵特征值问题的有效方法,可解决矩阵存在重特征值和密集特征值情况时的计算问题.块Jacboi-Davidson算法分为内外两层迭代,外层迭代计算矩阵特征对,内层迭代求解校正方程组,计算量主要花费是校正方程组的求解.针对校正方程的不精确求解,提出了几种构造预条件子的块不完全分解方法,并通过数值试验,对多种预条件子的效果进行比较.The block Jacobi - Davidson method is effective for computing large scale real symmetric eigenvalue problems, the issues addressed being the multiple or clustered eigenpairs. The block Jacobi - Davidson method includes outer and inner iterative. The outer iterativc is used to compute the pairs of eigenvalues while the inner iterative is used for the correction equations. The more time - consuming computation lies in solving the correction equations. To handle the imprecise solution of the correction equation, we propose several block incomplete factorization methods to obtain the pre - conditioning matrix. Numerical experiments were also carried out to compare the effect of these methods.

关 键 词：块Jacobi—Davidson方法 校正方程 不精确求解 预条件子块 

分 类 号：O241.6[理学—计算数学]