Semi-Definite Programming for Real Root Finding
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E93-A No.3 pp.636-639
- Publication Date
- 2010/03/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E93.A.636
- Type of Manuscript
- LETTER
- Category
- Digital Signal Processing
Authors
Keyword
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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},}
Copy
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 -
English
