Fast Algorithms for Manipulating Formal Power Series
The classical algorithms require O(n sup 3) operations to compute the first n terms in the reversion of a power series or the composition of two series, and O((n sup 2) log n) operations if the fast Fourier 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 O((n log n) sup 3/2) operations. In many cases of practical importance only O(n log n) operations are required. An application to root-finding methods which use inverse interpolation is described, some results on multivariate power series are stated, and several open questions are mentioned.
"The classical algorithms require O(n sup 3) operations to compute the first n terms in the reversion of a power series or the composition of two series, and O((n sup 2) log n) operations if the fast Fourier 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 O((n log n) sup 3/2) operations. In many cases of practical importance only O(n log n) operations are required. An application to root-finding methods which use inverse interpolation is described, some results on multivariate power series are stated, and several open questions are mentioned."@en
CARNEGIE-MELLON UNIV PITTSBURGH PA Dept. of COMPUTER SCIENCE.
This is a placeholder reference for a Organization entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.
This is a placeholder reference for a Topic entity, related to a WorldCat Entity. Over time, these references will be replaced with persistent URIs to VIAF, FAST, WorldCat, and other Linked Data resources.