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arXiv · 0904.2452

Effective Bounds for P-Recursive Sequences

Marc Mezzarobba·Bruno Salvy
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Abstract

We describe an algorithm that takes as input a complex sequence $(u_n)$ given by a linear recurrence relation with polynomial coefficients along with initial values, and outputs a simple explicit upper bound $(v_n)$ such that $|u_n| \leq v_n$ for all $n$. Generically, the bound is tight, in the sense that its asymptotic behaviour matches that of $u_n$. We discuss applications to the evaluation of power series with guaranteed precision.

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Marc Mezzarobba, Bruno Salvy. 2009-04-16. Effective Bounds for P-Recursive Sequences. https://doi.org/10.1016/j.jsc.2010.06.024

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