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Volume 3, Issue 2
The Computational Complexity of the Resultant Method for Solving Polynomial Equations

Xiao-Hua Xuan

J. Comp. Math., 3 (1985), pp. 161-166.

Published online: 1985-03

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  • 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 $$cd^2(log d+log\frac{1}{\mu}+loglog\frac{1}ε)$$, 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.

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@Article{JCM-3-161, author = {Xiao-Hua Xuan}, title = {The Computational Complexity of the Resultant Method for Solving Polynomial Equations}, journal = {Journal of Computational Mathematics}, year = {1985}, volume = {3}, number = {2}, pages = {161--166}, 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 $$cd^2(log d+log\frac{1}{\mu}+loglog\frac{1}ε)$$, 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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9613.html} }
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 -

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.

Xiao-Hua Xuan. (1985). The Computational Complexity of the Resultant Method for Solving Polynomial Equations. Journal of Computational Mathematics. 3 (2). 161-166. doi:
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