{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T14:25:44Z","timestamp":1740147944860,"version":"3.37.3"},"reference-count":15,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61203047","2012GGX10115"],"award-info":[{"award-number":["61203047","2012GGX10115"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Development Project of Science & Technology of Shandong Province","award":["61203047","2012GGX10115"],"award-info":[{"award-number":["61203047","2012GGX10115"]}]},{"DOI":"10.13039\/501100005358","name":"Linyi University","doi-asserted-by":"publisher","award":["61203047","2012GGX10115"],"award-info":[{"award-number":["61203047","2012GGX10115"]}],"id":[{"id":"10.13039\/501100005358","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods in Medicine"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We first give the style spectral decomposition of a special skew circulant matrix<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><\/mml:math>and then get the style decomposition of arbitrary skew circulant matrix by making use of the Kronecker products between the elements of first row in skew circulant and the special skew circulant<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>C<\/mml:mi><\/mml:mrow><\/mml:math>. Besides that, we obtain the singular value of skew circulant matrix as well. Finally, we deal with the optimal backward perturbation analysis for the linear system with skew circulant coefficient matrix on the base of its style spectral decomposition.<\/jats:p>","DOI":"10.1155\/2013\/707381","type":"journal-article","created":{"date-parts":[[2013,11,28]],"date-time":"2013-11-28T16:01:57Z","timestamp":1385654517000},"page":"1-7","source":"Crossref","is-referenced-by-count":8,"title":["On Optimal Backward Perturbation Analysis for the Linear System with Skew Circulant Coefficient Matrix"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1046-571X","authenticated-orcid":true,"given":"Juan","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematics, Linyi University, Linyi, Shandong 276000, China"},{"name":"Department of Mathematics, Shandong Normal University, Ji\u2019nan, Shandong 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhaolin","family":"Jiang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Linyi University, Linyi, Shandong 276000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nuo","family":"Shen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Linyi University, Linyi, Shandong 276000, China"},{"name":"Department of Mathematics, Shandong Normal University, Ji\u2019nan, Shandong 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jianwei","family":"Zhou","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Linyi University, Linyi, Shandong 276000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/3-540-45262-1_12","volume":"1988","year":"2001","journal-title":"Numerical Analysis and Its Applications"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01933178"},{"key":"3","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/0024-3795(93)90226-E","volume":"190","year":"1993","journal-title":"Linear Algebra and Its Applications"},{"key":"4","doi-asserted-by":"crossref","first-page":"767","DOI":"10.1137\/0613048","volume":"13","year":"1992","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-03-01534-5"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(02)00664-X"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/973407"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1109\/LSP.2006.884034"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/31.1800"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1109\/PROC.1971.8471"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1109\/83.760312"},{"issue":"2","key":"13","first-page":"162","volume":"12","year":"2003","journal-title":"Numerical Mathematics"},{"issue":"2","key":"14","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1137\/S0895479896297434","volume":"18","year":"1997","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"key":"15","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1145\/321406.321416","volume":"14","year":"1967","journal-title":"Journal of the ACM"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.compmedimag.2007.09.004"}],"container-title":["Computational and Mathematical Methods in Medicine"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2013\/707381.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2013\/707381.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/cmmm\/2013\/707381.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,21]],"date-time":"2017-06-21T23:21:38Z","timestamp":1498087298000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/cmmm\/2013\/707381\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":15,"alternative-id":["707381","707381"],"URL":"https:\/\/doi.org\/10.1155\/2013\/707381","relation":{},"ISSN":["1748-670X","1748-6718"],"issn-type":[{"type":"print","value":"1748-670X"},{"type":"electronic","value":"1748-6718"}],"subject":[],"published":{"date-parts":[[2013]]}}}