求解对称矩阵最大特征值的Barzilai-Borwein法

高维对称矩阵最大特征问题的求解是数学界中比较关注的问题之一。文章采用无约束优化方法进行求解,设计了非单调搜索的Barzilai-Borwein（BB）算法,数值算例显示该算法比单调线搜索最速下降法迭代次数更少,收敛速度快且相对误差小的良好计算性能。

Barzilai-Borwein Method for Extreme Symmetric Eigenvalue Problem

Solving maximum eigenvalue of large-scale symmetric matrix is an important topic in mathematics. This paper adopted the method of unrestrained optimization and proposed anon-monotone line search method Barzilai-Borwein（BB） algorithm. Nu- merical results show that iterations of this algorithm are less than that of momotone line search method, and that its convergence speed is faster and that its error is relatively small.