| 求非负矩阵最大特征值与特征向量的C-W方法 |
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| 引用本文： | 殷剑宏.求非负矩阵最大特征值与特征向量的C-W方法[J].合肥工业大学学报(自然科学版),2000,23(5):752-756. |
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| 作者姓名： | 殷剑宏 |
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| 作者单位： | 合肥工业大学,计算机与信息学院,安徽,合肥,230009 |
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| 摘 要： | 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.
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| 关 键 词： | 非负矩阵 最大特征值 不可约 C-W方法 |
| 修稿时间： | 2000-01-13 |
The Collatz-Wielandt method for finding the greatest eigenvalue and the greatest eigenvector of a nonnegative matrix |
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| YIN Jian-hong.The Collatz-Wielandt method for finding the greatest eigenvalue and the greatest eigenvector of a nonnegative matrix[J].Journal of Hefei University of Technology(Natural Science),2000,23(5):752-756. |
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| Authors: | YIN Jian-hong |
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| Abstract: | 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. |
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| Keywords: | nonnegative matrices greatest eigenvalue irreducibility C W method |
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