{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T02:01:29Z","timestamp":1760061689606},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2015,12]]},"abstract":"<jats:p> Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the polynomial and their existence has been proved in several different ways. However, the resulting algorithms for computing determinantal representations are computationally intensive. In this note, we present an algorithm that reduces a large part of the problem to linear algebra and discuss its numerical implementation. <\/jats:p>","DOI":"10.1142\/s0218196715500435","type":"journal-article","created":{"date-parts":[[2015,11,26]],"date-time":"2015-11-26T03:33:49Z","timestamp":1448508829000},"page":"1327-1336","source":"Crossref","is-referenced-by-count":4,"title":["Computing Hermitian determinantal representations of hyperbolic curves"],"prefix":"10.1142","volume":"25","author":[{"given":"Daniel","family":"Plaumann","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, Universit\u00e4t Konstanz, Zukunftskolleg, Box 216 78457 Konstanz, Germany"}]},{"given":"Rainer","family":"Sinn","sequence":"additional","affiliation":[{"name":"School of Mathematics, Georgia Institute of Technology, 686 Cherry Street NW, Atlanta, GA 30332, USA"}]},{"given":"David E.","family":"Speyer","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA"}]},{"given":"Cynthia","family":"Vinzant","sequence":"additional","affiliation":[{"name":"Department of Mathematics, North Carolina State University, Box 8205, Raleigh, North Carolina 27695, USA"}]}],"member":"219","published-online":{"date-parts":[[2015,12,30]]},"reference":[{"key":"S0218196715500435BIB001","first-page":"350","volume":"11","author":"Dixon A. C.","year":"1902","journal-title":"Math. Proc. Cambridge Philos. Soc."},{"key":"S0218196715500435BIB002","doi-asserted-by":"publisher","DOI":"10.1023\/A:1018915407202"},{"key":"S0218196715500435BIB003","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20155"},{"key":"S0218196715500435BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2011.01.007"},{"key":"S0218196715500435BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0411-0_19"},{"key":"S0218196715500435BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jsc.2013.05.004"},{"key":"S0218196715500435BIB007","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-04-12731-0"},{"key":"S0218196715500435BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/BF01445115"},{"key":"S0218196715500435BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-0411-0_23"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196715500435","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T15:16:18Z","timestamp":1565104578000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196715500435"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12]]},"references-count":9,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2015,12,30]]},"published-print":{"date-parts":[[2015,12]]}},"alternative-id":["10.1142\/S0218196715500435"],"URL":"https:\/\/doi.org\/10.1142\/s0218196715500435","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12]]}}}