New formula of 4-instant g-square finite difference (4IgSFD) applied to time-variant matrix inversion

As the time-variant matrix inversion is considered to be one of basic problems widely encountered in a variety of scientific and engineering fields, a new formula of 4-instant g-square finite difference (4IgSFD) for the time-variant matrix inversion is proposed and investigated, where g denotes the sampling gap. Note that the new formula is based on Taylor expansion instead of Lagrange interpolation, and has a truncation error of O(g²). According to this novel formula, a new discrete-time Zhang dynamics (DTZD) model termed 4IgSFD-type DTZD model is derived. The model uses the present and previous information to calculate the inverse of time-variant matrix for the next (or say, future) time instant with a high calculative precision. Then, the stability and convergence of the 4IgSFD-type DTZD model are guaranteed theoretically. Finally, we take different types of nonsingular time-variant matrices with different dimensions as testing examples and use different values of g in numerical experiments. The numerical experiment results show the efficacy of the 4IgSFD-type DTZD model for time-variant matrix inversion with truncation error being O(g³).