Perturbation analysis for the matrix least squares problem AXB=C

摘要

Let S and Ŝ be two sets of solutions to matrix least squares problem (LSP) AXB=C and the perturbed matrix LSP ÂX̂B̂=Ĉ, respectively, where Â=A+ΔA, B̂=B+ΔB, Ĉ=C+ΔC, and ΔA, ΔB, ΔC are all small perturbation matrices. For any given X∈S, we deduce general formulas of the least squares solutions X̂∈Ŝ 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.