@unpublished{B-An-Adaptive-Linear-Homotopy-Method-To-Approximate-Eigenpairs-Of-Homogeneous-Polynomial-Systems,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},
Author = {Paul Breiding},
Year = {2015},
Month = {12},
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 $f(\zeta)=\eta^{dâˆ’1}\zeta$. 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.},
Url = {http://arxiv.org/abs/1512.03284}
}