TY - JOUR
T1 - An effective implementation of a modified Laguerre method for the roots of a polynomial
AU - Cameron, Thomas R.
N1 - Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s11075-018-0641-9
DO - 10.1007/s11075-018-0641-9
M3 - Article
AN - SCOPUS:85058366407
SN - 1017-1398
VL - 82
SP - 1065
EP - 1084
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 3
ER -