Using Newton's method, we study the algorithm for computing the maximum eigenvalue and the corresponding positive eigenvectors of nonnegative irreducible matrices. Some improvement is made on the method due to Alfred Brauer for computing the maximum eigenvalue of irreducible nonnegative matrices. 本文研究了应用Newton法计算非负不可约距阵的最大特征值及相应正特征向量的算法,并对AlfredBrauer提出的计算不可约非负矩阵最大特征值的方法作了改进。