Abstract:Given a polynomial of degree and a bound on a condition number of , we present the first root-finding algorithms that return all its real and complex roots with a number of bit operations quasi-linear in log 2 ( ). More precisely, several condition numbers can be defined depending on the norm chosen on the coefficients of the polynomial. Let ( )We call the condition number associated with a perturbation of the the hyperbolic condition number ℎ , and the one associated with a perturbation of the the elliptic co… Show more
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