基于Gramian分解的对称半正定矩阵的正则化低秩逼近  

Regularized low rank approximation of symmetric positive semi-definite matrix based on Gramian decomposition

作　　者：张雪伟[1] 江祝灵 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》2015年第5期419-423,共5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：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。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 positive 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 experiments verify that the new method is feasible.

关 键 词：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 

分 类 号：O241.6[理学—计算数学]