| Abstract: | Under an assumption of distribution on zeros of the polynomials, we have given the estimate of computational cost for the resultant method. The result in that, in probability $1-mu$, the computational cost of the resultant method for finding $ε$-approximations of all zeros is at most $$cd^2(log d+logfrac{1}{mu}+loglogfrac{1}ε)$$, where the cost is measured by the number of f-evaluations. The estimate of cost can be decreased to $c(d^2logd+d^2logfrac{1}{mu}+dloglogfrac{1}ε)$ by combining resultant method with parallel quasi-Newton method. |
