求解大型特征值问题的块Davidson方法的精化技术

Refining-strategy of block Davidson method for solving large sparse eigenproblems

块Davidson方法是求解大型对称矩阵特征值问题的一种有效的方法.但对一些特征值问题,当Ritz值收敛以后,该方法并不能保证Ritz向量也同时收敛.因此,为加速块Davidson方法的收敛性,研究了块Davidson方法的重新开始技术,提出了精化块Davidson方法,并对精化块Davidson方法进行了收敛性分析.数值试验和理论分析均表明,新方法对计算大型对称矩阵的一些极端特征对是有效的.

Block Davidson method is very efficient for computing the eigenproblems of large symmetric matrices. To some eigenproblems, the corresponding Ritz vectors always converge very slowly when Ritz values have converged. So in order to improve the convergence of block Davidson method, a new algorithm is proposed,which improves the steps of restarting by using the refining - strategy. By analyzing the convergence of the new method and the numerical experiments, we can find that the new algorithm is very efficient for computing the extreme eigenpairs of large symmetric matrices.