arXiv:2610.41627v1 Announce Type: new Abstract: For computing the dominant eigenvalue and the corresponding eigenvector of a real and symmetric matrix, inspired by the parameterized power method and multistep iteration, we propose a two-sweep parameterized power method, and establish its convergence theory. To further improve the convergence speed of the new method, we use Gaussian process regression (GPR) to predict the quasi-optimal parameter and give a version of the proposed method based on GPR. Numerical experiments show that the two-sweep parameterized power method with quasi-optimal parameters outperforms some existing methods in terms of computing efficiency.