The case of a generalised linear discrete time system with infinite many   solutions
  In this article we study a class of generalised linear systems of difference equations with given non-consistent initial conditions and infinite many solutions. We take into consideration the case that the coefficients are square constant matrices with the leading coefficient singular. We provide optimal solutions and numerical examples to justify our theory. 
Nicholas Apostolopoulos, Fernando Ortega and Grigoris Kalogeropoulos
math.DS