A Unified Approach to Recurrence Algorithms
We show that the known methods for the computation of subdominant solutions of linear difference equations, either scalar recurrences or difference systems, are based on the replacement of an initial value problem by a system of linear equations expressed in boundary value form. This fact allows the development of a single uniform analysis for the convergence of the methods, and for the condition of the problem. Moreover, it is demonstrated that each of the resulting recurrence algorithms is mathematically equivalent to a type of triangular decomposition of the linear algebraic system, all algorithms being a form of either LU or UL factorization.
KeywordsMinimal Solution Fundamental Matrix Linear Difference Equation Linear Algebraic System Complementary Solution
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