Continuous and Discrete ZND Models with Aid of Eleven Instants for Complex QR Decomposition of Time-Varying Matrices

Jianrong Chen, Xiangui Kang () and Yunong Zhang ()
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Jianrong Chen: School of Public Health and Management, Youjiang Medical University for Nationalities, Baise 533000, China
Xiangui Kang: Guangdong Key Lab of Information Security, School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China
Yunong Zhang: Guangdong Key Lab of Information Security, School of Computer Science and Engineering, Sun Yat-sen University, Guangzhou 510006, China

Mathematics, 2023, vol. 11, issue 15, 1-18

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.

Keywords: complex QR decomposition; zeroing neural dynamics (ZND); dimensional reduction; Zhang et al discretization (ZeaD) formula (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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