对称半正定矩阵秩-1逼近  

Rank-1 approximation of symmetric positive semidefinite matrix

作　　者：张新俊[1] 段雪峰[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2014年第1期74-77,共4页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(11101100);广西自然科学基金(2012GXNSFBA053006)

摘　　要：为了得出一种有效的算法来求解对称半正定矩阵的秩-1逼近解,基于BFGS方法,构造了一种新的迭代算法。该算法利用X=YYT,Y∈Rn刻画可行集,将对称半正定矩阵的秩-1逼近问题转化为无约束优化问题,用BFGS方法求解无约束优化问题,并给出了2个数值例子。数值实验表明,此算法行之有效,且具有一定的应用价值。In order to get an effective algorithm to solve the rank-1 approximation of the symmetric positive semidefinite ma-trix.A new iterative algorithm is constructed based on BFGS method.The rank-1 approximation of the symmetric positive semidefinite matrix is transformed into an unconstrained optimization problem by using X =YY T ,Y ∈Rn to characterize the feasible set,and then the unconstrained optimization problem is solved by BFGS method.Finally,two numerical examples are given.Numerical experiments show that this algorithm is effective and has application value.

关 键 词：对称半正定矩阵 秩-1逼近 无约束优化 可行集 BFGS方法 

分 类 号：O241.6[理学—计算数学]