Perturbation analysis for the QX factorization for centrosymmetric matrices

Abstract

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.