论文信息 - Random Polynomials and Approximate Zeros of Newton's Method

Random Polynomials and Approximate Zeros of Newton's Method

In this paper the authors study the size of the set of “approximate zeros” for Newton’s method, for a randomly chosen polynomial over certain distributions. For a degree d monic polynomial with coefficients chosen uniformly and independently in the unit ball, the results of this paper show, for example, that the set of approximate zeros is at least $Cd^{(-1.5-\varepsilon)}$ for any positive $\varepsilon$, with C depending only on $\varepsilon$.

Joel Friedman

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