Continuous-Time Varying Complex QR Decomposition via Zeroing Neural Dynamics

QR decomposition (QRD) is of fundamental importance for matrix factorization in both real and complex cases. In this paper, by using zeroing neural dynamics method, a continuous-time model is proposed for solving the time-varying problem of QRD in real-time. The proposed dynamics use time derivative information from a known real or complex matrix. Furthermore, its theoretical analysis is provided to substantiate the convergence and effectiveness of solving the time-varying QRD problem. In addition, numerical experiments in four different-dimensional time-varying matrices show that the proposed model is effective for solving the time-varying QRD problem both in the case of a real or a complex matrix as input.

Automated summary

In this paper, a continuous-time model is proposed for solving the time-varying problem of QR decomposition using the zeroing neural dynamics method, utilizing time derivative information from a known real or complex matrix. Theoretical analysis and numerical experiments demonstrate the effectiveness and convergence of the proposed method for solving the time-varying QR decomposition problem in both real and complex cases.