Zeroing Neural Network for Pseudoinversion of an Arbitrary Time-Varying Matrix Based on Singular Value Decomposition
Maria I. Kornilova, Vladislav N. Kovalnogov, Ruslan V. Fedorov, М. М. Замалеев, Vasilios N. Katsikis, Spyridon D. Mourtas, Theodore E. Simos
Abstract
Many researchers have investigated the time-varying (TV) matrix pseudoinverse problem in recent years, for its importance in addressing TV problems in science and engineering. In this paper, the problem of calculating the inverse or pseudoinverse of an arbitrary TV real matrix is considered and addressed using the singular value decomposition (SVD) and the zeroing neural network (ZNN) approaches. Since SVD is frequently used to compute the inverse or pseudoinverse of a matrix, this research proposes a new ZNN model based on the SVD method as well as the technique of Tikhonov regularization, for solving the problem in continuous time. Numerical experiments, involving the pseudoinversion of square, rectangular, singular, and nonsingular input matrices, indicate that the proposed models are effective for solving the problem of the inversion or pseudoinversion of time varying matrices.