Paper Info
Title
An effective implementation of a modified Laguerre method for the roots of a polynomial
Abstract
Two common strategies for computing all roots of a polynomial with Laguerre’s method are explicit deflation and Maehly’s procedure. The former is only a semi-stable process and is not suitable for solving large degree polynomial equations. In contrast, the latter implicitly deflates the polynomial using previously accepted roots and is, therefore, a more practical strategy for solving large degree polynomial equations. However, since the roots of a polynomial are computed sequentially, this method cannot take advantage of parallel systems. In this article, we present an implementation of a modified Laguerre method for the simultaneous approximation of all roots of a polynomial. We provide a derivation of this method along with a detailed analysis of our algorithm’s initial estimates, stopping criterion, and stability. Finally, the results of several numerical experiments are provided to verify our analysis and the effectiveness of our algorithm.
Year
DOI
Venue
2019
10.1007/s11075-018-0641-9
Numerical Algorithms
Keywords
Field
DocType
Laguerre’s method, Polynomial roots, Mathematical software, 26C10, 65H04, 65Y20
Applied mathematics,Laguerre's method,Laguerre polynomials,Polynomial,Mathematical analysis,Degree of a polynomial,Mathematical software,Properties of polynomial roots,Mathematics
Journal
Volume
Issue
ISSN
82
3
1572-9265
Citations 
PageRank 
References 
0
0.34
10
Authors
1
Name
Order
Citations
PageRank
Thomas R. Cameron100.34