Semi-Definite Programming for Real Root Finding

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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.

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