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.
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Mezzarobba, M. (2012). A Note on the Space Complexity of Fast D-Finite Function Evaluation. In: Gerdt, V.P., Koepf, W., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2012. Lecture Notes in Computer Science, vol 7442. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32973-9_18
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