求非负矩阵最大特征值与特征向量的C-W方法

The Collatz-Wielandt method for finding the greatest eigenvalue and the greatest eigenvector of a nonnegative matrix

幂法是求矩阵最大特征值及最大特征向量的经典方法。依据 C- W函数及其理论 ,文章给出了求非负矩阵最大特征值及最大特征向量的有效迭代方法—— C- W方法。论证了其收敛性 ,给出了其误差估计 ,并与幂法进行了比较。C- W方法算法简单 ,不必附加任何收敛条件。计算结果表明 ,C- W法的收敛速度比幂法快。

Power Method is the conventional way for finding the greatest eigenvalue and the greatest eigenvector of a matrix.In this paper, a numerical method is introduced for calculating the greatest eigenvalue and the greatest eigenvector of a nonnegative matrix. The method is based upon the Collatz Wielandt(C W) function and called C W method. The convergence theorem of the algorithm is proven,and the absolute error is analyzed. Compared with Power Method, the new method is a simple way, and does not require any restrictive condition. The convergence rate obtained by C W method shows that the new method is more effective than Power Method.