Construction of algebraic and difference equations with a prescribed solution space
This paper studies the solution space of systems of algebraic and difference equations, given as auto-regressive (AR) representations A(σ)β(k) = 0, where σ denotes the shift forward operator and A(σ) is a regular polynomial matrix. The solution space of such systems consists of forward and backward propagating solutions, over a finite time horizon. This solution space can be constructed from knowledge of the finite and infinite elementary divisor structure of A(σ). This work deals with the inverse...