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Effective Bounds for P-Recursive Sequences

Marc Mezzarobba 1 Bruno Salvy 1
1 ALGORITHMS - Algorithms
Inria Paris-Rocquencourt
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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Submitted on : Friday, April 17, 2009 - 9:13:29 AM
Last modification on : Tuesday, January 11, 2022 - 11:16:23 AM

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Marc Mezzarobba, Bruno Salvy. Effective Bounds for P-Recursive Sequences. Journal of Symbolic Computation, Elsevier, 2010, 45 (10), pp.1075-1096. ⟨10.1016/j.jsc.2010.06.024⟩. ⟨inria-00376219⟩



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