An effective implementation of a modified Laguerre method for the roots of a polynomial
| Autor: | Thomas R. Cameron |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Polynomial
Laguerre's method Applied Mathematics Numerical analysis Stability (learning theory) 010103 numerical & computational mathematics 01 natural sciences 010101 applied mathematics Properties of polynomial roots ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION Theory of computation Laguerre polynomials Applied mathematics Degree of a polynomial 0101 mathematics Mathematics |
| Zdroj: | Numerical Algorithms. 82:1065-1084 |
| ISSN: | 1572-9265 1017-1398 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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