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

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


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.


Space Complexity Product Tree Hypergeometric Series Strip Mining Integer Multiplication 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© 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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