LIMIT BEHAVIOR OF SOLUTIONS OF SINGULAR DIFFERENCE EQUATIONS

Necessary and sufficient conditions for a solution {zk} of the difference equation Azk+1+Bzk = b, k ≥0, with A singular, to be a convergent sequence of vectors are given under a variety of assumptions. Theoretical results on iterative schemes for solving Ax = b by singular splittings, A = A+B, are given first. In particular, the case when A = A* and A is positive semi-definite is considered. Then applications to discrete control problems and backwards population projection are discussed. © 1979.