A note on the iterative solution of recurrence relations

Summary A class of Gauss-Seidel iteration schemes suitable for the stable generation of non-dominant solutions of certain third order linear recurrence relations is developed. The algorithms derived have two main advantages over existing algorithms which generally re-formulate the problem as the solution of a system of algebraic equations. Firstly, unlike existing algorithms, the algorithms developed in this paper automatically determine the size of the system to be solved in all cases and secondly they may be extended directly to an important class of nonlinear recurrence relations.