{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:54Z","timestamp":1740134514181,"version":"3.37.3"},"reference-count":6,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>The computation of the roots of positive definite matrices arises in nuclear magnetic resonance, control theory, lattice quantum chromo-dynamics (QCD), and several other areas of applications. The Cauchy integral theorem which arises in complex analysis can be used for computing<jats:italic>f(A)<\/jats:italic>, in particular the roots of<jats:italic>A<\/jats:italic>, where<jats:italic>A<\/jats:italic>is a square matrix. The Cauchy integral can be approximated by using the trapezoid rule. In this paper, we aim to give a brief overview of the computation of roots of positive definite matrices by employing integral representation. Some numerical experiments are given to illustrate the theoretical results.<\/jats:p>","DOI":"10.1155\/2012\/634698","type":"journal-article","created":{"date-parts":[[2012,1,24]],"date-time":"2012-01-24T16:02:38Z","timestamp":1327420958000},"page":"1-13","source":"Crossref","is-referenced-by-count":1,"title":["Approximation of the<i>p<\/i>th Roots of a Matrix by Using Trapezoid Rule"],"prefix":"10.1155","volume":"2012","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8720-1136","authenticated-orcid":true,"given":"Amir","family":"Sadeghi","sequence":"first","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4876-5462","authenticated-orcid":true,"given":"Ahmad Izani Md.","family":"Ismail","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia"}]}],"member":"311","reference":[{"journal-title":"Work Journal","year":"2005","key":"1"},{"journal-title":"MIMS EPrint","year":"2007","key":"5"},{"year":"1996","key":"4"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s11075-009-9357-1"},{"volume":"12","year":"2002","key":"8"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479801392697"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/634698.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/634698.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2012\/634698.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,8,2]],"date-time":"2016-08-02T16:53:04Z","timestamp":1470156784000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2012\/634698\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012]]},"references-count":6,"alternative-id":["634698","634698"],"URL":"https:\/\/doi.org\/10.1155\/2012\/634698","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2012]]}}}