The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Dans cette lettre, nous explorons le programme de relaxation semi-définie (SDR) pour trouver les racines réelles d'un polynôme réel. En utilisant le carré du polynôme, le problème est approximé à l'aide du cadre d'optimisation convexe et une racine réelle est estimée à partir du point minimum correspondant. Lorsqu’il n’y a qu’une seule racine réelle, la méthode SDR proposée donnera la solution exacte. Dans le cas de plusieurs racines réelles, la solution résultante peut être utilisée comme estimation initiale précise pour l’approche itérative visant à obtenir l’une des racines réelles. Grâce à la factorisation utilisant la racine obtenue, les racines réelles rappelant peuvent ensuite être résolues de manière séquentielle.
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Kenneth Wing Kin LUI, Hing Cheung SO, "Semi-Definite Programming for Real Root Finding" in IEICE TRANSACTIONS on Fundamentals,
vol. E93-A, no. 3, pp. 636-639, March 2010, doi: 10.1587/transfun.E93.A.636.
Abstract: In this Letter, we explore semi-definite relaxation (SDR) program for finding the real roots of a real polynomial. By utilizing the square of the polynomial, the problem is approximated using the convex optimization framework and a real root is estimated from the corresponding minimum point. When there is only one real root, the proposed SDR method will give the exact solution. In case of multiple real roots, the resultant solution can be employed as an accurate initial guess for the iterative approach to get one of the real roots. Through factorization using the obtained root, the reminding real roots can then be solved in a sequential manner.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E93.A.636/_p
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@ARTICLE{e93-a_3_636,
author={Kenneth Wing Kin LUI, Hing Cheung SO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Semi-Definite Programming for Real Root Finding},
year={2010},
volume={E93-A},
number={3},
pages={636-639},
abstract={In this Letter, we explore semi-definite relaxation (SDR) program for finding the real roots of a real polynomial. By utilizing the square of the polynomial, the problem is approximated using the convex optimization framework and a real root is estimated from the corresponding minimum point. When there is only one real root, the proposed SDR method will give the exact solution. In case of multiple real roots, the resultant solution can be employed as an accurate initial guess for the iterative approach to get one of the real roots. Through factorization using the obtained root, the reminding real roots can then be solved in a sequential manner.},
keywords={},
doi={10.1587/transfun.E93.A.636},
ISSN={1745-1337},
month={March},}
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TY - JOUR
TI - Semi-Definite Programming for Real Root Finding
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 636
EP - 639
AU - Kenneth Wing Kin LUI
AU - Hing Cheung SO
PY - 2010
DO - 10.1587/transfun.E93.A.636
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E93-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 2010
AB - In this Letter, we explore semi-definite relaxation (SDR) program for finding the real roots of a real polynomial. By utilizing the square of the polynomial, the problem is approximated using the convex optimization framework and a real root is estimated from the corresponding minimum point. When there is only one real root, the proposed SDR method will give the exact solution. In case of multiple real roots, the resultant solution can be employed as an accurate initial guess for the iterative approach to get one of the real roots. Through factorization using the obtained root, the reminding real roots can then be solved in a sequential manner.
ER -