一种求解大型稀疏对称矩阵（极端）特征值问题的有效算法

AN EFFECTIVE ALGORITHM FOR SOLVING (THE LARGEST OR LOWEST) EIGENPROBLEMS OF LARGE SPARSE SYMMETRIC MATRICES

提出一种求解大型稀疏对称矩阵几个最大（最小）特征值和相应特征向量的迭代块ＤＬ（即ＤａｖｉｄｓｏｎＬａｎｃｚｏｓ）算法并且讨论了迭代块ＤＬ算法的收敛率

An iterative block DL (i.e. Davidson Lanczos) algorithm is presented for computing a few of the largest (or lowest) eigenvalues and corresponding eigenvectors of very large sparse symmetric matrices. It′s convergence rate is also discussed. it overcomes the disadvantages of the DL method which cann′t find multiple or clustered eigenvalues, and the convergence speed of the mesent method is far faster than the DL method. Numerical results are compared whith those by the DL algorithm in a few experiments which exhibit a sharp superiority of the new approach.