Zhang Matrix Found as an Exception with its Time-Dependent Pseudoinverse Unsolvable by Getz-Masden Dynamic System

Abstract

Two classes of time-dependent matrices are proposed and investigated in this paper in terms of their pseudoinverses solving. On one hand, the pseudoinverse of Getz-Masden matrix can be solved by Getz-Masden dynamic system (GMDS) effectively and accurately. On the other hand, the GMDS can not solve for the pseudoinverse of Zhang matrix, as found and shown in this paper. Besides, for the purpose of obtaining the discrete-time GMDS and illustrating the phenomena, Euler forward formula and four-point ZeaD (Zhang et al discretization) formula are adopted to discretize the continuous-time GMDS. After getting the two discrete-time GMDS models, the solving situations of Getz-Masden matrix and Zhang matrix are compared.