TY - JOUR
T1 - The Computational Complexity of the Resultant Method for Solving Polynomial Equations
AU - Xiao-Hua Xuan
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 - <p style="text-align: justify;">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.</p>