Fast computation of the Nth root
type: Item
instance of: scholarly article
title: Fast computation of the Nth root
zbMATH Open document ID: 0687.65052
DOI: 10.1016/0898-1221(89)90024-2
author: K. Appert
publication date: 1989-01-01T00:00:00Z
review text: A new class of iterative methods for computing a differentiable function is proposed, which is based on Padé approximation to Taylor's series of the function. It leads to a faster algorithm than Newton's method for \(x^{1/N}\) and a different interpretation of Newton's method. This algorithm uses 3rd degree approximation of continued fraction expansion to Taylor's series for \(x^{1/N}\), with adaptive expansion point for every iteration. Its major computational cost is \(O[(2 \log_ 2 N)(\log_ 4 M)]\) multiplications asymptotically, M is the number of precision bits desired, as opposed to existing bound of \(O[(2 \log_ 2 N)(\log_ 2 M)]\) for Newton's method.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65D20
Mathematics Subject Classification ID: 41A21
zbMATH DE Number: 4126596
zbMATH Keywords: Nth root
zbMATH Keywords: iterative methods
zbMATH Keywords: differentiable function
zbMATH Keywords: Padé approximation
zbMATH Keywords: Taylor's series
zbMATH Keywords: Newton's method
zbMATH Keywords: computational cost
describes a project that uses: Algorithm 524
describes a project that uses: cheney-kincaid
MaRDI profile type: Publication
full work available at URL: 0898-1221(89)90024-2
OpenAlex ID: W1971190483
cites work: Q3902384
cites work: Optimal starting approximations for Newton's method
cites work: Q4076249
cites work: Q3798123
cites work: Best Rational Starting Approximations and Improved Newton Iteration for the Square Root
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4126596