核范数和谱范数下广义Sylvester方程最小二乘问题的有效算法
发布时间:2018-12-21 07:21
【摘要】:本文从数值角度讨论Schatten q-范数下的广义Sylvester方程约束最小二乘问题min x∈s‖N∑i=1A_iXB_i—C‖_q,其中S为闭凸约束集合,Schatten q-范数定义为‖M‖_q~q=∑_(i=1)~nσ_i~q(M),其中σ_i(M)为M∈R~(n×n)的奇异值.该问题的几类特殊情形在图像处理、控制论等领域有广泛的应用.q=2即Frobenius范数下该问题已被充分研究,故本文着重讨论q=1,+∞,即核范数和谱范数下该问题的数值求解.采用的数值方法是非精确标准容易执行的部分非精确交替方向法,并结合奇异值阈值算法,Moreau-Yosida正则化算法,谱投影算法和LSQR算法等求解相应子问题.给出算法的收敛性证明,并用数值算例验证其高效可行性.
[Abstract]:In this paper, we discuss the constrained least squares problem of generalized Sylvester equation under Schatten q-norm from a numerical point of view, where S is a closed convex constrained set. The Schatten q-norm is defined as the singular value of M 鈭,
本文编号:2388563
[Abstract]:In this paper, we discuss the constrained least squares problem of generalized Sylvester equation under Schatten q-norm from a numerical point of view, where S is a closed convex constrained set. The Schatten q-norm is defined as the singular value of M 鈭,
本文编号:2388563
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