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| Zitatschlüssel | B-An-Adaptive-Linear-Homotopy-Method-To-Approximate-Eigenpairs-Of-Homogeneous-Polynomial-Systems |
|---|---|
| Autor | Paul Breiding |
| Jahr | 2015 |
| Monat | 12 |
| Zusammenfassung | 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. |