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- Title
Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices.
- Authors
Chen, Jianrong; Kang, Xiangui; Zhang, Yunong
- Abstract
The problem of QR decomposition is considered one of the fundamental problems commonly encountered in both scientific research and engineering applications. In this paper, the QR decomposition for complex-valued time-varying matrices is analyzed and investigated. Specifically, by applying the zeroing neural dynamics (ZND) method, dimensional reduction method, equivalent transformations, Kronecker product, and vectorization techniques, a new continuous-time QR decomposition (CTQRD) model is derived and presented. Then, a novel eleven-instant Zhang et al discretization (ZeaD) formula, with fifth-order precision, is proposed and studied. Additionally, five discrete-time QR decomposition (DTQRD) models are further obtained by using the eleven-instant and other ZeaD formulas. Theoretical analysis and numerical experimental results confirmed the correctness and effectiveness of the proposed continuous and discrete ZND models.
- Subjects
MATRIX decomposition; KRONECKER products; NUMERICAL analysis
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 15, p3354
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11153354