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A Note on the Space Complexity of Fast D-Finite Function Evaluation

Marc Mezzarobba 1 
1 ARIC - Arithmetic and Computing
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : We state and analyze a generalization of the ''truncation trick'' suggested by Gourdon and Sebah to improve the performance of power series evaluation by binary splitting. It follows from our analysis that the values of D-finite functions (i.e., functions described as solutions of linear differential equations with polynomial coefficients) may be computed with error bounded by 2^(-p) in time Ο(p*(lg p)^(3+o(1))) and space Ο(p). The standard fast algorithm for this task, due to Chudnovsky and Chudnovsky, achieves the same time complexity bound but requires Θ(p*lg p) bits of memory.
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Submitted on : Sunday, September 23, 2012 - 11:28:46 AM
Last modification on : Monday, May 16, 2022 - 4:58:02 PM
Long-term archiving on: : Monday, December 24, 2012 - 2:40:11 AM


Distributed under a Creative Commons CC0 - Public Domain Dedication 4.0 International License




Marc Mezzarobba. A Note on the Space Complexity of Fast D-Finite Function Evaluation. CASC - Computer Algebra in Scientific Computing, Sep 2012, Maribor, Slovenia. pp.212-223, ⟨10.1007/978-3-642-32973-9_18⟩. ⟨hal-00687818v2⟩



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