A fast algorithm for reversion of power series
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- by Fredrik Johansson PDF
- Math. Comp. 84 (2015), 475-484 Request permission
Abstract:
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + M\!M(n^{1/2})))$ operations where $M(n)$ and $M\!M(n)$ are the costs of polynomial and matrix multiplication, respectively. This matches the asymptotic complexity of an algorithm of Brent and Kung, but we achieve a constant factor speedup whose magnitude depends on the polynomial and matrix multiplication algorithms used. Benchmarks confirm that the algorithm performs well in practice.References
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Additional Information
- Fredrik Johansson
- Affiliation: Research Institute for Symbolic Computation, Johannes Kepler University, 4040 Linz, Austria
- MR Author ID: 999321
- Email: fredrik.johansson@risc.jku.at
- Received by editor(s): August 22, 2011
- Received by editor(s) in revised form: April 26, 2013
- Published electronically: May 6, 2014
- Additional Notes: This work was supported by Austrian Science Fund (FWF) grant Y464-N18.
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Math. Comp. 84 (2015), 475-484
- MSC (2010): Primary 68W30
- DOI: https://doi.org/10.1090/S0025-5718-2014-02857-3
- MathSciNet review: 3266971