求解大型对称特征值问题的改进块Jaeobi—Davidson方法

块Jacobi—Davidson方法是求解对称矩阵重或密集特征值问题的一种有效方法．为了提高其整体收敛速度，应用动态压缩技术，提出了动态压缩的块Jacobi—Davidson方法；为了计算大型对称矩阵的内部特征对，本文将调和Rayleigh—Ritz方法与块Jacobi—Davidson方法结合，提出了调和块Jacobi—Davidson方法，并将动态压缩技术应用于调和块Jacobi—Davidson方法，给出了动态压缩的调和块Jacobi—Davidson方法．数值结果表明，动态压缩的块Jacobi—Davidson方法优于块Jacobi—David—son方法，动态压缩的调和块Jacobi—Davidson方法能有效计算大型对称矩阵的内部重或密集特征值．

The Improved Block Jacobi-Davidson Method for Solving Large Symmetric Eigenvalue Problems

Block Jacobi-Davidson method （BJD） is very efficient for computing the multiple or clustered eigenpairs of the symmetric eigenproblems. In order to improve its overall convergence speed, this paper applies the dynarnie deflation technique and presents the dynamic deflation version of the method （DBJD）. In order to computer interior eigenvalues, we apply the block Jacobi-Davidson method to the harmonic Rayleigh- Ritz procedure and propose the harmonic block Jacobi-Davidson method （HBJD）. Finally, we also apply the dynamic deflation technique to the harmonic block Jacobi-Davidson method （DHBJD）. Numerical experiments show that the improved algorithms is more efficient, moreover, the HBJD and the DHBJD is very efficient for computing the multiple or clustered interior eigenpairs of the symmetric eigenproblems.