Structured condition numbers for Sylvester matrix equation with parameterized quasiseparable matrices

• Published in: Communications on Analysis and Computation 2023-09, Vol.1 (3), p.183-213
• Main Authors: Diao, Huaian, Li, Lei, Meng, Qingle
• Format: Article
• Language: English
• ISSN: 2837-0562; 2837-0562
• DOI: 10.3934/cac.2023011

This paper considers the structured perturbation analysis of Sylve-ster matrix equation with low-rank structures. When the coefficient matrix and the right-hand side of Sylvester matrix equation are $ \{1;1\} $-quasiseparable matrices, we propose the structured condition numbers and obtain explicit expressions for these structured condition numbers using the general parameter representation and the tangent-based Givens-vector representation. By comparing different condition numbers of Sylvester matrix equation, we analyze their mathematical relationship. Numerical experiments demonstrate that the structured condition number is significantly smaller than the unstructured condition number when the elements in the general representation of $ \{1;1\} $-quasiseparable matrices have different scales. This suggests that structured algorithms for low-rank structured matrix equations can effectively reduce the loss of numerical solution accuracy.