TY - JOUR T1 - The Computational Complexity of the Resultant Method for Solving Polynomial Equations JO - Journal of Computational Mathematics VL - 2 SP - 161 EP - 166 PY - 1985 DA - 1985/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9613.html KW - AB -

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 $$cd^2(log d+log\frac{1}{\mu}+loglog\frac{1}ε)$$, where the cost is measured by the number of f-evaluations. The estimate of cost can be decreased to $c(d^2logd+d^2log\frac{1}{\mu}+dloglog\frac{1}ε)$ by combining resultant method with parallel quasi-Newton method.