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
2015年
5期
419-423
,共5页
张雪伟%江祝灵%段雪峰
張雪偉%江祝靈%段雪峰
장설위%강축령%단설봉
对称半正定矩阵%正则化低秩逼近%非线性共轭梯度法%Gramian分解
對稱半正定矩陣%正則化低秩逼近%非線性共軛梯度法%Gramian分解
대칭반정정구진%정칙화저질핍근%비선성공액제도법%Gramian분해
symmetric positive semi-definite matrix%regularized low rank approximation%nonlinear conjugate gradient meth-od%Gramian decomposition
针对对称半正定矩阵的正则化低秩逼近问题，基于对称半正定矩阵的 Gramian 分解，将对称半正定矩阵的正则化低秩逼近问题转化为等价的无约束优化问题，并构造非线性共轭梯度方法求解转化后的无约束优化问题。数值实验验证了新方法的可行性。
針對對稱半正定矩陣的正則化低秩逼近問題，基于對稱半正定矩陣的 Gramian 分解，將對稱半正定矩陣的正則化低秩逼近問題轉化為等價的無約束優化問題，併構造非線性共軛梯度方法求解轉化後的無約束優化問題。數值實驗驗證瞭新方法的可行性。
침대대칭반정정구진적정칙화저질핍근문제，기우대칭반정정구진적 Gramian 분해，장대칭반정정구진적정칙화저질핍근문제전화위등개적무약속우화문제，병구조비선성공액제도방법구해전화후적무약속우화문제。수치실험험증료신방법적가행성。
The regularized low rank approximation of symmetric positive semi-definite matrix is studied.Based on Gramian decomposition of a symmetric positive semi-definite matrix,the regularized low rank approximation of the symmetric posi-tive semi-definite matrix problem is transformed into an equivalent unconstrained optimization problem,and the nonlinear conjugate gradient method is constructed to solve the equivalent unconstrained optimization problem.The numerical experi-ments verify that the new method is feasible.
