SIAM Journal on Matrix Analysis and Applications, Volume 44, Issue 4, Page 1693-1708, December 2023.
Abstract. 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.

中文翻译：

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通过交替 SDP 的谱范数中算子的克罗内克积逼近

《SIAM 矩阵分析与应用杂志》，第 44 卷，第 4 期，第 1693-1708 页，2023 年 12 月。
摘要。将矩阵空间上的线性算子分解或逼近为克罗内克乘积之和，在矩阵方程和低秩建模中发挥着重要作用。Frobenius 范数中的逼近问题通过奇异值分解得到了一个众所周知的解。然而，对于线性算子来说更自然的谱范数逼近问题更具挑战性。特别是，弗罗贝尼乌斯范数解在谱范数方面可能远非最佳。我们描述了一种基于半定规划的交替优化方法，以获得谱范数的高质量近似，并且我们提出了计算实验来说明我们的方法的优点。