Abstract
In this paper, we study a bound on the real roots of a polynomial by Lagrange. From known results in the literature, it follows that Lagrange’s bound is also a bound on the absolute positiveness of a polynomial. A simple \(O(n\log n)\) algorithm described in Mehlhorn-Ray (2010) can be used to compute the bound. Our main result is that this is optimal in the real RAM model. Our paper explores the tradeoff between improving the quality of bounds on absolute positiveness and their computational complexity.
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Acknowledgement
The authors would like to express their gratitude to Dr. Prashant Batra and the referees for their invaluable comments and suggestions.
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Prabhakar, S.N., Sharma, V. (2016). A Lower Bound for Computing Lagrange’s Real Root Bound. In: Gerdt, V., Koepf, W., Seiler, W., Vorozhtsov, E. (eds) Computer Algebra in Scientific Computing. CASC 2016. Lecture Notes in Computer Science(), vol 9890. Springer, Cham. https://doi.org/10.1007/978-3-319-45641-6_28
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DOI: https://doi.org/10.1007/978-3-319-45641-6_28
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