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An adaptive linear homotopy method to approximate eigenpairs of homogeneous polynomial systems
Citation key B-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 $f(\zeta)=\eta^d−1\zeta$. 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.
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