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

  • Marc Mezzarobba
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7442)

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 \(\mathrm{O} (p (\lg p)^{3 + o (1)})\) and space O (p). The standard fast algorithm for this task, due to Chudnovsky and Chudnovsky, achieves the same time complexity bound but requires \(\mathrm\Theta (p \lg p)\) bits of memory.

Keywords

Lution Univer 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Marc Mezzarobba
    • 1
  1. 1.Inria, AriC, LIP (UMR 5668 CNRS-ENS Lyon-Inria-UCBL)France

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