# Is the Fujiwara bound the most precise bound on maximum absolute value of complex roots of real polynomials?

Is the Fujiwara bound the most precise bound on maximum absolute value of complex roots of real polynomials ? Or does it exist some improved version for this special case of real polynomials ?

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This wikipedia page discusses some of the improvements of the Fujiwara bound.

If the coefficients of your polynomial are all positive then the Eneström-Kakeya bound is often very good. See, for example, this paper (PDF). There are some generalizations, for instance when the coefficients lie in a given sector symmetric about the positive real axis.

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