Truncation and manipulation of multivariate power series
type: Item
instance of: scholarly article
title: Truncation and manipulation of multivariate power series
zbMATH Open document ID: 0627.65003
DOI: 10.1016/0377-0427(86)90236-0
author: G. W. Forbes
published in: Journal of Computational and Applied Mathematics
publication date: 1986-01-01T00:00:00Z
review text: A new approach to the manipulation of power series in several variables is described. It is based on the new concept of weighted truncation: The series \(f(x)=\sum_{r\in {\mathbb{N}}^ n}f_ rx^ r\quad (x\in {\mathbb{R}}^ n)\) with coefficients \(f_ r\) is truncated by retaining only those terms with \(w\cdot r\leq M\), where \(w\in {\mathbb{N}}^ n\) is a prescribed weight vector and M is a positive constant. Algorithms using this approach are then discussed for various operations with power series: addition, multiplication, division, evaluation of a function of a series, such as the logarithm, the exponential, the sine, etc., and, finally, composition and reversion. In connection with function evaluation, often the coefficients of \(f^*(x)=\sum w_ ix_ i\partial f/\partial x_ i\) are aimed at first, and \(f_ r=f^*_ r/(w\cdot r)\) is then used to obtain those of f.
Mathematics Subject Classification ID: 65B10
Mathematics Subject Classification ID: 26B12
Mathematics Subject Classification ID: 26E05
Mathematics Subject Classification ID: 41A58
zbMATH DE Number: 4020291
zbMATH Keywords: Taylor series
zbMATH Keywords: algebraic operations
zbMATH Keywords: power series in several variables
zbMATH Keywords: weighted truncation
zbMATH Keywords: logarithm
zbMATH Keywords: exponential
zbMATH Keywords: composition
zbMATH Keywords: reversion
zbMATH Keywords: function evaluation
reviewed by: Martin H. Gutknecht
MaRDI profile type: Publication
full work available at URL: 0377-0427(86)90236-0
OpenAlex ID: W2007161711
cites work: Expansions in power series by computer
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cites work: Q4198061
cites work: Operations on power series and polynomials
cites work: Methods and Applications of Power Series
cites work: Computing with Formal Power Series
description: scientific article; zbMATH DE number 4020291