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The  QX  factorization of the centrosymmetric matrix is a structure-preserving  QR  factorization proposed by Konrad Burnik. In this paper, we first propose a sufficient condition for the uniqueness of this decomposition. Then, using the refined matrix equation approach, we derive the first-order normwise perturbation bounds convenient for computation for the  QX  factorization. Using the matrix-vector equation approach and the modified matrix-vector equation approach, we obtain the optimal first-order normwise perturbation bounds. Moreover, the normwise condition numbers for the  QX  factorization are also presented. Some numerical examples are given to illustrate our theoretical results.

Perturbation analysis for the QX factorization for centrosymmetric matrices