Time-Varying Complex Zhang Matrix (ZM) with Its Pseudoinverse not Solvable Directly by Getz-Masden (GM) Dynamic System

摘要

The concepts of Getz-Masden matrix (GMM) and Zhang matrix (ZM) are extended to complex time-varying matrix situation in this paper. For the complex time-varying matrix, the matrix whose pseudoinverse can be obtained by Getz-Masden dynamic system (GMDS) is called GMM, and the other matrix is called ZM. GMDS can be regarded as a special case of Zhang neural network (ZNN), which has good performance in solving time-varying problems. The Adams-Bashforth (AB) methods of one-step, two-step and three-step are used for discretization of continuous GMDS to obtain the discrete GMDS models. After getting the three models, they are respectively used to obtain the solutions of Getz-Masden matrix pseudoinverses problem (GMMPP) and Zhang matrix pseudoinverses problem (ZMPP), and the results are analyzed and compared.