{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:13Z","timestamp":1740134533099,"version":"3.37.3"},"reference-count":17,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"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":[[2014]]},"abstract":"<jats:p>New algorithms are presented about the principal square root of an<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>n<\/mml:mi><mml:mo>\u00d7<\/mml:mo><mml:mi>n<\/mml:mi><\/mml:mrow><\/mml:math>matrix<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><\/mml:math>. In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed.<\/jats:p>","DOI":"10.1155\/2014\/613840","type":"journal-article","created":{"date-parts":[[2014,6,18]],"date-time":"2014-06-18T20:15:52Z","timestamp":1403122552000},"page":"1-8","source":"Crossref","is-referenced-by-count":1,"title":["Inversion Free Algorithms for Computing the Principal Square Root of a Matrix"],"prefix":"10.1155","volume":"2014","author":[{"given":"Nicholas","family":"Assimakis","sequence":"first","affiliation":[{"name":"Department of Electronic Engineering, Technological Educational Institute of Central Greece, 3rd km Old National Road Lamia-Athens, 35100 Lamia, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3555-6610","authenticated-orcid":true,"given":"Maria","family":"Adam","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Biomedical Informatics, University of Thessaly, 2-4 Papasiopoulou Street, 35100 Lamia, Greece"}]}],"member":"311","reference":[{"doi-asserted-by":"publisher","key":"4","DOI":"10.1007\/s11075-004-6709-8"},{"doi-asserted-by":"publisher","key":"6","DOI":"10.1137\/050643374"},{"doi-asserted-by":"publisher","key":"7","DOI":"10.2307\/2007992"},{"doi-asserted-by":"publisher","key":"10","DOI":"10.2307\/2002785"},{"issue":"4","key":"12","first-page":"467","volume":"1","year":"1993","journal-title":"Neural, Parallel & Scientific Computations"},{"issue":"9","key":"13","doi-asserted-by":"crossref","first-page":"820","DOI":"10.1109\/TAC.1987.1104721","volume":"32","year":"1987","journal-title":"IEEE Transactions on Automatic Control"},{"doi-asserted-by":"publisher","key":"14","DOI":"10.1016\/0898-1221(88)90034-X"},{"key":"5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/978-3-642-36803-5_12","volume-title":"Blocked schur algorithms for computing the matrix square root","volume":"7782","year":"2013"},{"key":"8","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1115\/1.3658902","volume":"83","year":"1961","journal-title":"Journal of Basic Engineering, Transactions of the ASME D"},{"issue":"3","key":"16","first-page":"659","volume":"27","year":"2005","journal-title":"Songklanakarin Journal of Science and Technology"},{"doi-asserted-by":"publisher","key":"9","DOI":"10.1109\/TAC.1985.1103822"},{"issue":"5","key":"11","doi-asserted-by":"crossref","first-page":"677","DOI":"10.1109\/TAC.1976.1101321","volume":"21","year":"1976","journal-title":"IEEE Transactions on Automatic Control"},{"doi-asserted-by":"publisher","key":"17","DOI":"10.1137\/S1064827594277041"},{"year":"2012","key":"1"},{"key":"2","first-page":"22","volume":"3","year":"2009","journal-title":"The Open Applied Informatics Journal"},{"doi-asserted-by":"publisher","key":"3","DOI":"10.1155\/2014\/417623"},{"issue":"5","key":"15","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1109\/TAC.1970.1099549","volume":"15","year":"1970","journal-title":"IEEE Transactions on Automatic Control"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/613840.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/613840.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2014\/613840.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T11:08:33Z","timestamp":1498129713000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2014\/613840\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":17,"alternative-id":["613840","613840"],"URL":"https:\/\/doi.org\/10.1155\/2014\/613840","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2014]]}}}