{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:08:37Z","timestamp":1750306117052,"version":"3.41.0"},"reference-count":8,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2017,2,22]],"date-time":"2017-02-22T00:00:00Z","timestamp":1487721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2017,2,22]]},"abstract":"<jats:p>Polynomials eigenvalue problems with structured matrix polynomials arise in many applications. The standard way to solve polynomial eigenvalue problems is through the classical Frobenius companion linearizations, which may not retain the structure of the matrix polynomial. Particularly, the structure of the symmetric matrix polynomials can be lost, while from the computational point of view, it is advisable to construct a linearization which preserves the symmetry structure. Recently, new families of block-Kronecker pencils have been introduced in [5]. Applying block-Kronecker pencils, we present structure-preserving strong linearizations for symmetric matrix polynomials. When the matrix polynomial has an odd degree, these linearizations are strong regardless of whether the matrix polynomial is regular or singular. Additionally, we construct structure-preserving strong linearizations for regular symmetric matrix polynomials of even degree under some simple nonsingularity conditions.<\/jats:p>","DOI":"10.1145\/3055282.3055292","type":"journal-article","created":{"date-parts":[[2017,2,27]],"date-time":"2017-02-27T13:06:52Z","timestamp":1488200812000},"page":"167-169","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Constructing symmetric structure-preserving strong linearizations"],"prefix":"10.1145","volume":"50","author":[{"given":"Heike","family":"Fassbender","sequence":"first","affiliation":[{"name":"Technische Universit\u00e4t Braunschweig, Braunschweig, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Javier","family":"P\u00e9rez","sequence":"additional","affiliation":[{"name":"The University of Manchester, Manchester, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nikta","family":"Shayanfar","sequence":"additional","affiliation":[{"name":"Technische Universit\u00e4t Braunschweig, Braunschweig, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,2,22]]},"reference":[{"key":"e_1_2_1_1_1","volume-title":"Linearizations of Hermitian matrix polynomials preserving the sign characteristic. Submitted for publication","author":"Bueno M. I.","year":"2016","unstructured":"M. I. Bueno , F. M. Dopico , S. Furtado . Linearizations of Hermitian matrix polynomials preserving the sign characteristic. Submitted for publication , 2016 . M. I. Bueno, F. M. Dopico, S. Furtado. Linearizations of Hermitian matrix polynomials preserving the sign characteristic. Submitted for publication, 2016."},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2015.03.032"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2014.07.007"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/090772927"},{"key":"e_1_2_1_5_1","volume-title":"Block Kronecker linearizations of matrix polynomials and their backward errors. Submitted for publication. Also available as MIMS EPrint","author":"Dopico F. M.","year":"2016","unstructured":"F. M. Dopico , P. Lawrence , J. P\u00e9rez , P. Van Dooren . Block Kronecker linearizations of matrix polynomials and their backward errors. Submitted for publication. Also available as MIMS EPrint 2016 .34, School of Mathematics, The University of Manchester , UK , 2016. F. M. Dopico, P. Lawrence, J. P\u00e9rez, P. Van Dooren. Block Kronecker linearizations of matrix polynomials and their backward errors. Submitted for publication. Also available as MIMS EPrint 2016.34, School of Mathematics, The University of Manchester, UK, 2016."},{"key":"e_1_2_1_6_1","volume-title":"Symmetric and skew-symmetric block-Kronecker linearizations. Submitted for publication. Also available as arXiv:1606.01766","author":"Fassbender H.","year":"2016","unstructured":"H. Fassbender , J. P\u00e9rez , N. Shayanfar . Symmetric and skew-symmetric block-Kronecker linearizations. Submitted for publication. Also available as arXiv:1606.01766 , 2016 . H. Fassbender, J. P\u00e9rez, N. Shayanfar. Symmetric and skew-symmetric block-Kronecker linearizations. Submitted for publication. Also available as arXiv:1606.01766, 2016."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/050646202"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1137\/050628362"}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3055282.3055292","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3055282.3055292","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:36:37Z","timestamp":1750217797000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3055282.3055292"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,22]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2017,2,22]]}},"alternative-id":["10.1145\/3055282.3055292"],"URL":"https:\/\/doi.org\/10.1145\/3055282.3055292","relation":{},"ISSN":["1932-2240"],"issn-type":[{"type":"print","value":"1932-2240"}],"subject":[],"published":{"date-parts":[[2017,2,22]]},"assertion":[{"value":"2017-02-22","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}