12 2015.

Paper abstract bibtex

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@UNPUBLISHED{B-An-Adaptive-Linear-Homotopy-Method-To-Approximate-Eigenpairs-Of-Homogeneous-Polynomial-Systems, TITLE={An adaptive linear homotopy method to approximate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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