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SIAM Journal on Numerical Analysis
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SIAM Journal on Numerical Analysis
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Khovanskii–Rolle Continuation for Real Solutions
Foundations of Computational Mathematics
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ACM Transactions on Mathematical Software (TOMS)
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Given a polynomial system f, a fundamental question is to determine if f has real roots. Many algorithms involving the use of infinitesimal deformations have been proposed to answer this question. In this article, we transform an approach of Rouillier, Roy, and Safey El Din, which is based on a classical optimization approach of Seidenberg, to develop a homotopy based approach for computing at least one point on each connected component of a real algebraic set. Examples are presented demonstrating the effectiveness of this parallelizable homotopy based approach.