An efficient second‐order neural network model for computing the Moore–Penrose inverse of matrices

Abstract

Abstract The computation of the Moore–Penrose inverse is widely encountered in science and engineering. Due to the parallel‐processing nature and strong‐learning ability, the neural network has become a promising approach to solving the Moore–Penrose inverse recently. However, almost all the existing neural networks for matrix inversion are based on the gradient‐descent (GD) method, whose main drawbacks are slow convergence and sensitivity to learning parameters. Moreover, there is no unified neural network to compute the Moore–Penrose inverse for both the full‐rank matrix and rank‐deficient matrix. In this paper, an efficient second‐order neural network model with the improved Newton's method is proposed to obtain the accurate Moore–Penrose inverse of an arbitrary matrix by one epoch without any learning parameter. Compared with the GD‐based neural networks for Moore–Penrose inverse computation, the proposed model converges faster and has lower complexity. Furthermore, through in‐depth derivation, the neural network for computing the Moore–Penrose inverse is well interpretable. Numerical studies and application to the random matrix inversion in multiple‐input multiple‐output detection are provided to validate the efficiency of the proposed model for solving the Moore–Penrose inverse.

Keywords

• arbitrary matrix
• improved Newton’s method
• Moore‐Penrose inverse
• neural network
• second‐order model