- The paper investigates and characterises the source of numerical instability in the deconvolution procedures of generating-unit models. An upper bound on the round-off errors in the conventional deconvolution process is derived. An important contribution of the paper is the interpretation of the deconvolution relationship in terms of a linear nonhomogeneous matrix-vector recurrence. This allows the development of a decoupled recurrence procedure by application of methods originally developed for solving ordinary difference equations in boundary value problems. An alternative method called quasi-Schur decoupling is also developed and is shown to be more suitable under specific conditions. The paper also presents an overall strategy for applying these tools in an efficient manner to obtain guaranteed accurate results.