A Note on the Space Complexity of Fast D-Finite Function Evaluation
Symbolic Computation
2012-09-25 v1
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 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 \Theta(p*lg p) bits of memory.
Cite
@article{arxiv.1209.5097,
title = {A Note on the Space Complexity of Fast D-Finite Function Evaluation},
author = {Marc Mezzarobba},
journal= {arXiv preprint arXiv:1209.5097},
year = {2012}
}