@UNPUBLISHED{B-An-Adaptive-Linear-Homotopy-Method-To-Approximate-Eigenpairs-Of-Homogeneous-Polynomial-Systems,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}
}

{"_id":"LryBjjvF4mkq4trPW","bibbaseid":"breiding-anadaptivelinearhomotopymethodtoapproximateeigenpairsofhomogeneouspolynomialsystems-2015","downloads":0,"creationDate":"2017-01-04T12:11:10.486Z","title":"An adaptive linear homotopy method to approximate eigenpairs of homogeneous polynomial systems","author_short":["Breiding, P."],"year":2015,"bibtype":"unpublished","biburl":"http://www3.math.tu-berlin.de/algebra/static/papers.parsed.bib","bibdata":{"bibtype":"unpublished","type":"unpublished","title":"An adaptive linear homotopy method to approximate eigenpairs of homogeneous polynomial systems","url":"http://arxiv.org/abs/1512.03284","author":[{"firstnames":["Paul"],"propositions":[],"lastnames":["Breiding"],"suffixes":[]}],"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 ","month":"12","bibtex":"@UNPUBLISHED{B-An-Adaptive-Linear-Homotopy-Method-To-Approximate-Eigenpairs-Of-Homogeneous-Polynomial-Systems,\r\n TITLE={An adaptive linear homotopy method to approximate eigenpairs of homogeneous polynomial systems},\r\n URL={http://arxiv.org/abs/1512.03284},\r\n AUTHOR={Paul Breiding},\r\n YEAR={2015},\r\n 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. },\r\n MONTH={12}\r\n}\r\n\r\n","author_short":["Breiding, P."],"key":"B-An-Adaptive-Linear-Homotopy-Method-To-Approximate-Eigenpairs-Of-Homogeneous-Polynomial-Systems","id":"B-An-Adaptive-Linear-Homotopy-Method-To-Approximate-Eigenpairs-Of-Homogeneous-Polynomial-Systems","bibbaseid":"breiding-anadaptivelinearhomotopymethodtoapproximateeigenpairsofhomogeneouspolynomialsystems-2015","role":"author","urls":{"Paper":"http://arxiv.org/abs/1512.03284"},"downloads":0,"html":""},"search_terms":["adaptive","linear","homotopy","method","approximate","eigenpairs","homogeneous","polynomial","systems","breiding"],"keywords":[],"authorIDs":[],"dataSources":["mFLw2PzriqAWWFuqX"]}