Work

Rigorous perturbation bounds for the QX decomposition for centrosymmetric matrices

Year: 2025

Type: article

Abstract: Konrad Burnik suggests a structure-preserving QR factorization for centrosymmetric matrices, known as QX factorization. In this article, we obtain the explicit expressions for rigorous perturbation bounds of the QX factorization when the original matrix is perturbed, either norm-wise or component-wise. First, using the matrix-equation approach, weak rigorous perturbation bounds are derived. Then, strong rigorous perturbation bounds are obtained by combining the modified matrix-vector equation approach with the strategy for the Lyapunov majorant function and the Banach fixed-point theorem. The mixed and component-wise condition numbers and their upper bounds are also explicitly expressed. Numerical tests illustrate the validity of the obtained results.

Source: Linear and Multilinear Algebra

DOI: 10.1080/03081087.2025.2464652

Authors: Aamir Farooq, Rewayat Khan, Uzma Rani, M. Tariq Rahim

Institutions: Zhejiang Normal University, Technical University of Liberec, Sabancı Üniversitesi, Abbottabad University of Science and Technology

Language: English

Topic: Matrix Theory and Algorithms

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Türkiye Bilimsel ve Teknolojik Araştırma Kurumu

Awards: G1885236558, G3957037266, G4296967674