2022/09/29 by Zihao Li, Lek‐Heng Lim, Li, Zihao +1
Computer Science · Engineering · #15A10 #52A27 #65F18 #65F55 #Blind Source Separation Techniques #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.2209.14954
openalex publication_date 2022/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show that the global minimum solution of ‖ A - BXC ‖ can be found in closed-form with singular value decompositions and generalized singular value decompositions for a variety of constraints on X involving rank, norm, symmetry, two-sided product, and prescribed eigenvalue. This extends the solution of Friedland--Torokhti for the generalized rank-constrained approximation problem to other constraints as well as provides an alternative solution for rank constraint in terms of singular value decompositions. For more complicated constraints on X involving structures such as Toeplitz, Hankel, circulant, nonnegativity, stochasticity, positive semidefiniteness, prescribed eigenvector, etc, we prove that a simple iterative method is linearly and globally convergent to the global minimum solution.