Root squaring using level-index arithmetic
type: Item
instance of: scholarly article
title: Root squaring using level-index arithmetic
zbMATH Open document ID: 0688.65031
DOI: 10.1007/BF02241860
author: C. W. Clenshaw
author: Peter R. Turner
published in: Computing
publication date: 1989-01-01T00:00:00Z
review text: The symmetric level-index (SLI) system is a system for representing numbers, which eases the monitoring of precision while avoiding the problem associated with overflow and underflow. In SLI system any real number X is represented by its mapping in computer x, a sign s(X) and a reciprocation indicator r(X), so that we have \(X=s(X)\phi (x)^{r(X)},\) where the generalized exponential function \(\phi\) is defined by \(\phi (x)=x,\quad x\in [0,1),\) and \(\phi (x)=e^{\phi (x-1)},\quad x\geq 1.\) The authors discuss the essentials of SLI and apply it to Graeffe's root squaring method for finding zeros of polynomials. Numerical results from test examples are given.
Mathematics Subject Classification ID: 65H05
Mathematics Subject Classification ID: 65G99
zbMATH DE Number: 4128303
zbMATH Keywords: numerical examples
zbMATH Keywords: symmetric level-index system
zbMATH Keywords: Graeffe's root squaring method
zbMATH Keywords: zeros of polynomials
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02241860
OpenAlex ID: W171774305
description: scientific article; zbMATH DE number 4128303