Effective bounds for P-recursive sequences

• Autores: Marc Mezzarobba, Bruno Salvy
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 45, Nº 10, 2010, págs. 1075-1096
• Idioma: inglés
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• Resumen

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