求解对称矩阵极端特征值的Chebyshev-PBL方法

Chebyshev-PBL Method for Solving Extreme Eignvalues of Symmetric Matrix

为了加速预处理块 Lanczos方法的收敛性 ,本文采用组合 Chebyshev迭代和预处理块 Lanczos方法 ,提出了求解大型对称稀疏矩阵极端特征值的一种新方法—— Chebyshev-PBL方法。数值结果表明 ,新方法对计算大型对称稀疏矩阵的几个最大 (或最小 )

The preconditioned Lanczos (PL) method is a very effective method for computing one extreme eigenvalue of large symmetric sparse matrix. The preconditioned block Lanczos (PBL) method is the improvement of the PL method which can compute several extreme eigenvalues of large symmetric sparse matrix. In some case, for example the wanted eigenvalue′s distribution is bad, the efficiency of the PBL method is low. The Chebyshev iteration is one of the most used techniques for improving the extreme eigenvalue′s convergence. In order to accelerate the convergence rate of the PBL method, a new method, i.e. Chebyshev PBL method is presented for computing the extreme eigenvalues of large symmetric sparse matrices. The new method combines the Chebyshev iteration with the PBL method. Numerical experiments show that the Chebyshev PBL method is very effective for computing the extreme eigenvalues of large symmetric sparse metrices.