论文标题
通过交替的SDP，在光谱规范中运算符的Kronecker产品近似
Kronecker Product Approximation of Operators in Spectral Norm via Alternating SDP
论文作者
论文摘要
线性操作员在矩阵空间上作为Kronecker产品的总和在矩阵方程和低级别建模中起重要作用。 Frobenius Norm中的近似问题通过奇异值分解接受了众所周知的解决方案。但是，光谱规范中的近似问题对线性操作员来说更为自然，这更具挑战性。特别是，Frobenius Norm解决方案在光谱规范中远非最佳。我们描述了一种基于半决赛编程的交替优化方法，以获得光谱规范中的高质量近似值，并提出了计算实验，以说明我们方法的优势。
The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The approximation problem in Frobenius norm admits a well-known solution via the singular value decomposition. However, the approximation problem in spectral norm, which is more natural for linear operators, is much more challenging. In particular, the Frobenius norm solution can be far from optimal in spectral norm. We describe an alternating optimization method based on semidefinite programming to obtain high-quality approximations in spectral norm, and we present computational experiments to illustrate the advantages of our approach.
