Email this article ON THE COMPUTATION OF LAGRANGE’S QUADRATIC BOUND FOR POSITIVE ROOTS OF POLYNOMIALS
- Authors: Akritas Alkiviadis G -1, Malaschonok G.I.2
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Affiliations:
- University of Thessaly
- Tambov State University named after G.R. Derzhavin
- Issue: Vol 21, No 6 (2016)
- Pages: 1933-1937
- Section: Articles
- URL: https://ogarev-online.ru/2686-9667/article/view/365966
- DOI: https://doi.org/10.20310/1810-0198-2016-21-6-1933-1937
- ID: 365966
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Abstract
Lagrange’s quadratic bound, LQ , on the values of the positive roots of polynomials consists of two parts. Sorting of one-dimensional arrays is used in the second part of the Lagrange algorithm in all known implementations. We propose to change this part of the algorithm and to avoid the sort. The computing time of the second part as is currently implemented is O(n∙ log(n)) . With our improvement we reduce the computing time of the second step of LQ to O(n) .
About the authors
- Akritas Alkiviadis G
University of Thessaly
Email: akritas@uth.gr
Doctor of philosophy, Professor of the Electrical and Computer Engineering Department Volos, Greece
Gennadi Ivanovich Malaschonok
Tambov State University named after G.R. Derzhavin
Email: malaschonok@ya.ru
Doctor of Physics and Mathematics, Professor of the Functional Analysis Department Tambov, the Russian Federation
References
Lagrange Joseph-Louis Sur la r´esolution des ´equations num´eriques, 1767. In: M´emoires de l’ Acad´emie Royale des Sciences et des Belle-Lettres de Berlin, (1769), 23, 539-578. This is in vol. 2 of J. A. Serret’s Œuvres de Lagrange. Lagrange Joseph-Louis Trait´e de la r´esolution des ´equations num´eriques de tous les degr´es. Paris, 1808. This is vol. 8 of J. A. Serret’s Œuvres de Lagrange. Serret, J. A. Œuvres de Lagrange. Paris: Gauthier-Villars, 1879. Akritas A.G., Strzebo´nski A.W., Vigklas P.S. Lagrange’s Bound on the Values of the Positive Roots of Polynomials. Submitted.
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