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06-12-2019 | Original Paper | Issue 3/2020

Numerical Algorithms 3/2020

New zeroing neural dynamics models for diagonalization of symmetric matrix stream

Journal:
Numerical Algorithms > Issue 3/2020
Authors:
Yunong Zhang, Huanchang Huang, Min Yang, Yihong Ling, Jian Li, Binbin Qiu
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Abstract

In this paper, the problem of diagonalizing a symmetric matrix stream (or say, time-varying matrix) is investigated. To fulfill our goal of diagonalization, two error functions are constructed. By making the error functions converge to zero with zeroing neural dynamics (ZND) design formulas, a continuous ZND model is established and its effectiveness is then substantiated by simulative results. Furthermore, a Zhang et al. discretization (ZeaD) formula with high precision is developed to discretize the continuous ZND model. Thus, a new 5-point discrete ZND (DZND) model is further proposed for diagonalization of matrix stream. Theoretical analyses prove the stability and convergence of the 5-point DZND model. In addition, simulative experiments are carried out, of which the results substantiate not only the efficacy of the proposed 5-point DZND model but also its higher computational precision as compared with the conventional Euler-type and 4-point DZND models for diagonalization of symmetric matrix stream.

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