Real-domain QR decomposition models employing zeroing neural network and time-discretization formulas for time-varying matrices

Abstract This study investigated the problem of QR decomposition for time-varying matrices. We transform the original QR decomposition problem into an equation system using its constraints. Then, we propose a continuous-time QR decomposition (CTQRD) model by applying zeroing neural network method, equivalent transformations, Kronecker product, and vectorization techniques. Subsequently, a high-precision ten-instant Zhang et al discretization (ZeaD) formula is proposed. A ten-instant discrete-time QR decomposition model is also proposed by using the ten-instant ZeaD formula to discretize the CTQRD model. Moreover, three discrete-time QR decomposition models are proposed by applying three other ZeaD formulas, and three examples of QR decomposition are presented. The experimental results confirm the effectiveness and correctness of the proposed models for the QR decomposition of time-varying matrices.

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