A Parallel Preconditioned Power Method for the Maximum Eigenvalue of Real Symmetric Matrices

摘要

This paper presents the preconditioned method for parallel solution to the maximum eigenvalue of real symmetric matrices by the power method. It is based on the low complexity information transmission of the banded matrix satisfying some bandwidth condition. We reduce the large-scale real symmetric dense matrix to a banded matrix by parallel Householder transformation, then solve the maximum eigenvalue of the banded matrix by the power method. Finally, some numerical experiments on Lenovo ShenTeng 1800 cluster are shown for the different bandwidth matrices formed by matrix transformation. Comparing it with the calculation results by the power method without pretreatment ,it is shown that if the bandwidth is the widest under a bandwidth condition our method has the highest parallel efficiency.