Perturbation analysis for the matrix least squares problem A X B = C.

Let S and S ̂ be two sets of solutions to matrix least squares problem (LSP) A X B = Cand the perturbed matrix LSP A ̂ X ̂ B ̂ = C ̂, respectively, where A ̂ = A + Δ A, B ̂ = B + Δ B, C ̂ = C + Δ C, and Δ A, Δ B, Δ C are all small perturbation matrices. For any given X ∈ S, we deduce general formulas of the least squares solutions X ̂ ∈ S ̂ that are closest to X under appropriated norms, meanwhile, we present the corresponding distances between them. With the obtained results, we derive perturbation bounds for the nearest least squares solutions. At last, a numerical example is provided to verify our analysis. [ABSTRACT FROM AUTHOR]