0 N Log N Superscript 3 2 Algorithms For Composition And Reversion Of Power Series
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0 N Log N Superscript 3 2 Algorithms For Composition And Reversion Of Power Series
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Author : Richard P. Brent
language : en
Publisher:
Release Date : 1975
0 N Log N Superscript 3 2 Algorithms For Composition And Reversion Of Power Series written by Richard P. Brent and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
Topics In Computational Complexity And The Analysis Of Algorithms
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Author : Richard P. Brent
language : en
Publisher:
Release Date : 1980
Topics In Computational Complexity And The Analysis Of Algorithms written by Richard P. Brent and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Algorithms categories.
O N Log N Sup 3 2 Algorithms For Composition And Reversion Of Power Series
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Author : R. P. Brent
language : en
Publisher:
Release Date : 1975
O N Log N Sup 3 2 Algorithms For Composition And Reversion Of Power Series written by R. P. Brent and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with categories.
0 N Log N 3 2 Algorithms For Composition And Reversion Of Power Series
DOWNLOAD
Author : Richard P. Brent
language : en
Publisher:
Release Date : 1975
0 N Log N 3 2 Algorithms For Composition And Reversion Of Power Series written by Richard P. Brent and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Algorithms categories.
Physics Briefs
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Author :
language : en
Publisher:
Release Date : 1989
Physics Briefs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Physics categories.
Fast Algorithms For Manipulating Formal Power Series
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Author : Richard P. Brent
language : en
Publisher:
Release Date : 1976
Fast Algorithms For Manipulating Formal Power Series written by Richard P. Brent and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Algorithms categories.
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.
On The Complexity Of Composition And Generalized Composition Of Power Series
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Author : Richard P. Brent
language : en
Publisher:
Release Date : 1978
On The Complexity Of Composition And Generalized Composition Of Power Series written by Richard P. Brent and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Algorithms categories.
Let F(x) = f1x + f2(x)(x) + ... be a formal power series over a field Delta. Let F superscript 0(x) = x and for q = 1,2, ..., define F superscript q(x) = F superscript (q-1) (F(x)). The obvious algorithm for computing the first n terms of F superscript q(x) is by the composition position analogue of repeated squaring. This algorithm has complexity about log 2 q times that of a single composition. The factor log 2 q can be eliminated in the computation of the first n terms of (F(x)) to the q power by a change of representation, using the logarithm and exponential functions. We show the factor log 2 q can also be eliminated for the composition problem. F superscript q(x) can often, but not always, be defined for more general q. We give algorithms and complexity bounds for computing the first n terms of F superscript q(x) whenever it is defined.