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LU Decomposition by Using ZNN Method and ZeaD Formulas

Research and Reports on Mathematics.

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LU Decomposition by Using ZNN Method and ZeaD Formulas

In this paper, by employing the Zhang neural network (ZNN) method, effective continuous-time LU decomposition (CTLUD) model is firstly proposed, analyzed, and investigated for solving the time-varying LU decomposition problem. Then, for the convenience of digital hardware realization, this paper proposes three discrete-time models by using Euler, 4-instant Zhang et al. discretization (ZeaD), and 8-instant ZeaD formulas to discretize the proposed CTLUD model, respectively. Furthermore, the proposed models are wont to perform the LU decomposition of three time-varying matrices with different dimensions. Results indicate that the proposed models are effective for solving the time-varying LU decomposition problem, and therefore the 8-instant ZeaD LU decomposition model has the very best precision among the three discrete-time models.

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