Abstract: In this report, I will introduce an algorithm for calculating the maximum eigenvalue of a matrix, as well as its algorithm design and proof of convergence rate. We are familiar with Google using PageRank algorithm. PageRank algorithm is based on the power method to calculate the eigenvector corresponding to the maximum eigenvalue of the matrix to sort the target web pages. Based on several existing algorithms, power method, Aitken method, inverse power method, and Rayleigh quotient iteration method. There are some unavoidable shortcomings. However, Chen’s algorithm solves these problems.