Rapid Dual Integral Neural Dynamic for Dynamic Matrix Square Root Finding

Abstract

The dynamic matrix square root (DMSR) problem is a recurring nonlinear challenge in many engineering disciplines. Although the original zeroing neural network (OZNN) shows potential for handling such problems, it faces challenges in robustness and convergence. To address these limitations, we developed a simplified activation function, the simplified signal power activation function (SSPAF), which accelerates convergence. Building on this, we introduced a dual integral enhancement term, leading to the design of the rapid dual integral neural dynamic (R-DIND) model to further enhance convergence accuracy, speed, and robustness. Mathematically, the R-DIND model aligns more closely with calculus principles, showcasing unique advantages over existing ZNN models. Theoretical analysis and extensive experiments demonstrated that the R-DIND model has inherent structural advantages over the RNDAC model. Results showed that the R-DIND model improves residual precision from $10^{-2}$ to $10^{-6}$ under the same noise conditions. Furthermore, its robustness and applicability were confirmed when applied to higher-order and more complex matrix problems with harmonic noise.

Keywords

• Matrix square root
• noise tolerant
• dynamic problems
• zeroing neural network
• dual integral
• activation function