Title

An efficient algorithm for deriving summation identities from mutual recurrences

Document Type

Article

Date of Original Version

6-1-2012

Abstract

This paper closes an algorithmic problem of summing a set of mutual recurrence relations with constant coefficients. Given an order d system of the form A(n) = \sum-{i = 1}^dM-iA(n-i)+\, G(n), where A, G: → Km and M1,..., Md Mm(K) for some field K and natural number m, this algorithm computes the sum \sum-{i = 0}^n{A(i)} as a K-linear combination of A(n),..., A(n - d), the initial conditions and sums of the inhomogeneous term G(n). The runtime of this algorithm is shown to be polynomial in m and d.

Publication Title

Discrete Mathematics, Algorithms and Applications

Volume

4

Issue

2

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