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arXiv · 1806.03554

A fast algorithm for solving linearly recurrent sequences

Seung Gyu Hyun·Stephen Melczer·Catherine St-Pierre
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Abstract

We present an algorithm which computes the $D^{th}$ term of a sequence satisfying a linear recurrence relation of order $d$ over a field $K$ in $O( \mathsf{M}(\bar d)\log(D) + \mathsf{M}(d)\log(d))$ operations in $K$, where $\bar d \leq d$ is the degree of the squarefree part of the annihilating polynomial of the recurrence and $\mathsf{M}$ is the cost of polynomial multiplication in $K$. This is a refinement of the previously optimal result of $O( \mathsf{M}(d)\log(D) )$ operations, due to Fiduccia.

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Seung Gyu Hyun, Stephen Melczer, Catherine St-Pierre. 2018-06-09. A fast algorithm for solving linearly recurrent sequences. https://arxiv.org/abs/1806.03554

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