Design and Analysis of an Inverse-Free Zeroing Neural Network Model for Matrix Decomposition

Matrix decomposition (MD), which factorizes a matrix into the product of two lower-dimensional matrices, is fundamental in many computational tasks. Although classical methods such as singular value decomposition (SVD) offer high precision, their reliance on complex operations—particularly matrix inversion—limits deployment on hardware-constrained platforms like neuromorphic or analog systems. To address this, we propose an inverse-free zeroing neural network (IFZNN) model under a neurodynamic framework for solving MD problems. Unlike existing ZNN-based models, IFZNN avoids matrix inversion entirely, reducing computational complexity and enhancing suitability for real-time and low-power hardware implementation. Theoretical analysis rigorously proves its global and exponential convergence. In the experimental section, a series of tests validate the feasibility, stability, and robustness of the IFZNN model. We compare IFZNN with mainstream neurodynamic models (i.e., advanced methods in the current domain) in terms of convergence speed, accuracy, and efficiency. For instance, compared to the gradient-based neural network (GNN) model, IFZNN exhibits faster convergence rates. Applied to real-world MD tasks, the model reduces the root mean square error (RMSE) of the reconstructed matrix from 1.3713 to 0.1176, corresponding to a 91.42% improvement. The optimization objective decreases from 1.2602 × 10⁷ to 9.2607 × 10⁴, indicating a 99.27% reduction. These experimental findings corroborate the theoretical insights, emphasizing that IFZNN offers an effective, hardware-friendly solution for MD tasks. Its structure is particularly suited for edge-computing scenarios that require efficient, real-time deployment.