桂林电子科技大学学报
桂林電子科技大學學報
계림전자과기대학학보
JOURNAL OF GUILIN UNIVERSITY OF ELECTRONIC TECHNOLOGY
2014年
1期
74-77
,共4页
对称半正定矩阵%秩-1逼近%无约束优化%可行集%BFGS方法
對稱半正定矩陣%秩-1逼近%無約束優化%可行集%BFGS方法
대칭반정정구진%질-1핍근%무약속우화%가행집%BFGS방법
symmetric positive semidefinite matrix%rank-1 approximation%unconstrained optimization%feasible set%BFGS method
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 =YY T ,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。
為瞭得齣一種有效的算法來求解對稱半正定矩陣的秩-1逼近解,基于 BFGS方法,構造瞭一種新的迭代算法。該算法利用X =YY T ,Y ∈Rn 刻畫可行集,將對稱半正定矩陣的秩-1逼近問題轉化為無約束優化問題,用 BFGS方法求解無約束優化問題,併給齣瞭2箇數值例子。數值實驗錶明,此算法行之有效,且具有一定的應用價值。
위료득출일충유효적산법래구해대칭반정정구진적질-1핍근해,기우 BFGS방법,구조료일충신적질대산법。해산법이용X =YY T ,Y ∈Rn 각화가행집,장대칭반정정구진적질-1핍근문제전화위무약속우화문제,용 BFGS방법구해무약속우화문제,병급출료2개수치례자。수치실험표명,차산법행지유효,차구유일정적응용개치。
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.
