An adaptive linear homotopy method to approximate eigenpairs of homogeneous polynomial systems. Breiding, P. 12 2015.
Paper abstract bibtex Let $f=(f_1,...,f_n)$ be a system of n complex homogeneous polynomials in n variables of degree $d\ge 2$. We call $(\zeta,\eta)\in\mathbb P^n\setminus\{[0:1]\}$ an $h$-eigenpair of $f$ if $f(\zeta)=\eta^{d−1}\zeta$. We describe a randomized algorithm to compute approximations of $h$-eigenpairs of polynomial systems. Assuming random input, the average number of arithmetic operations it performs is polynomially bounded in the input size.
@UNPUBLISHED{B-An-Adaptive-Linear-Homotopy-Method-To-Approximate-Eigenpairs-Of-Homogeneous-Polynomial-Systems,
TITLE={An adaptive linear homotopy method to approximate eigenpairs of homogeneous polynomial systems},
URL={http://arxiv.org/abs/1512.03284},
AUTHOR={Paul Breiding},
YEAR={2015},
ABSTRACT={Let $f=(f_1,...,f_n)$ be a system of n complex homogeneous polynomials in n variables of degree $d\ge 2$. We call $(\zeta,\eta)\in\mathbb P^n\setminus\{[0:1]\}$ an $h$-eigenpair of $f$ if $f(\zeta)=\eta^{d−1}\zeta$. We describe a randomized algorithm to compute approximations of $h$-eigenpairs of polynomial systems. Assuming random input, the average number of arithmetic operations it performs is polynomially bounded in the input size. },
MONTH={12}
}
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