NUMERICAL-METHODS FOR STABLE IMPLEMENTATION OF GENERATING-UNIT DECONVOLUTION

The paper investigates and characterises the source of numerical insta bility in the deconvolution procedures of generating-unit models. An u pper bound on the round-off errors in the conventional deconvolution p rocess is derived. An important contribution of the paper is the inter pretation of the deconvolution relationship in terms of a linear nonho mogeneous matrix-vector recurrence. This allows the development of a d ecoupled recurrence procedure by application of methods originally dev eloped for solving ordinary difference equations in boundary value pro blems. An alternative method called quasi-Schur decoupling is also dev eloped and is shown to be more suitable under specific conditions. The paper also presents an overall strategy for applying these tools in a n efficient manner to obtain guaranteed accurate results.