Discrete RKZD (Reciprocal-Kind Zhang Dynamics) Algorithm Solving Time-Independent Linear Matrix-Vector Equation (TILMVE) Simplified from Time-Dependent Situation
Zhang, Yunong; Lu, Ji; Mao, Mingzhi; Li, Shuai (2023-09-18)
IEEE
18.09.2023
Y. Zhang, J. Lu, M. Mao and S. Li, "Discrete RKZD (Reciprocal-Kind Zhang Dynamics) Algorithm Solving Time-Independent Linear Matrix-Vector Equation (TILMVE) Simplified from Time-Dependent Situation," 2023 42nd Chinese Control Conference (CCC), Tianjin, China, 2023, pp. 116-121, doi: 10.23919/CCC58697.2023.10240545
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202405284019
https://urn.fi/URN:NBN:fi:oulu-202405284019
Tiivistelmä
Abstract
We present a continuous reciprocal-kind Zhang dynamics (RKZD) model for solving the time-dependent linear matrixvector equation. On the basis of the model, we deduce its simplified form for solving the time-independent linear matrix-vector equation (TILMVE). Subsequently, for more efficient computation and easier implementation in digital hardware, we utilize Euler forward difference formula (EFDF) to discretize the continuous RKZD model, resulting in a discrete RKZD algorithm. Finally, numerical experimental results attest to the feasibility and high effectiveness of the discrete RKZD algorithm for solving TILMVE. Comparisons with the discrete gradient neural network (or termed discrete gradient dynamics), Jacobi iteration, as well as Gauss-Seidel iteration highlight the superior convergence properties of the discrete RKZD algorithm.
We present a continuous reciprocal-kind Zhang dynamics (RKZD) model for solving the time-dependent linear matrixvector equation. On the basis of the model, we deduce its simplified form for solving the time-independent linear matrix-vector equation (TILMVE). Subsequently, for more efficient computation and easier implementation in digital hardware, we utilize Euler forward difference formula (EFDF) to discretize the continuous RKZD model, resulting in a discrete RKZD algorithm. Finally, numerical experimental results attest to the feasibility and high effectiveness of the discrete RKZD algorithm for solving TILMVE. Comparisons with the discrete gradient neural network (or termed discrete gradient dynamics), Jacobi iteration, as well as Gauss-Seidel iteration highlight the superior convergence properties of the discrete RKZD algorithm.
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