For given complex matrices $A$ and $B$, I want to find \begin{align} \min_{D_1,D_2} \|D_1 A D_2-B\|_F \end{align} where $D_1,D_2$ are diagonal matrices with each diagonal entry on the unit circle. What is the most relevant algorithm for this problem? Thanks.
2026-05-14 07:37:26.1778744246
Find the closest matrix with equivalence
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There may be a sleek direct solution to the problem, though the quadratic nature of both the objective and constraints give me pause. As a starting point, notice that if you fix either $D_1$ or $D_2$, you can optimize the other one by solving independent orthogonal procrustes problems for each diagonal entry; one computational approach is then to alternate fixing $D_1$ and finding $D_2$, and vice-versa.