The numerical solution of linear recurrence relations

By analysing the effect of rounding error on linear recurrence relations having exponential-type complementary solutions, the distribution of two-point boundary conditions most likely to specify a well-conditioned problem is deduced. An intuitive explanation is derived by extending the Bernouilli method of polynomial factorisation to the case of variable coefficients. The replacement of specific boundary conditions by a knowledge of the relative behaviour of the particular and complementary solutions is discussed, and illustrated by examples.