## Fast Algorithms for Manipulating Formal Power Series

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Citations: | 105 - 9 self |

### BibTeX

@MISC{Brent_fastalgorithms,

author = {R P. Brent and H T Kung},

title = {Fast Algorithms for Manipulating Formal Power Series },

year = {}

}

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### Abstract

The classical algorithms require order n ~ operations to compute the first n terms in the reversion of a power series or the composition of two series, and order nelog n operations if the fast Founer transform is used for power series multiplication In this paper we show that the composition and reversion problems are equivalent (up to constant factors), and we give algorithms which require only order (n log n) ~/2 operations In many cases of practical importance only order n log n operations are required, these include certain special functions of power series and power series solution of certain differential equations Applications to root-finding methods which use inverse interpolation and to queueing theory are described, some results on multivariate power series are stated, and several open questions are mentioned.