{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:26Z","timestamp":1740134486821,"version":"3.37.3"},"reference-count":20,"publisher":"Wiley","license":[{"start":{"date-parts":[[2007,1,1]],"date-time":"2007-01-01T00:00:00Z","timestamp":1167609600000},"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":[[2007]]},"abstract":"<jats:p>We first recall some properties of infinite tridiagonal matrices considered as matrix transformations in sequence spaces of the forms<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:msub><mml:mi>s<\/mml:mi><mml:mi>\u03be<\/mml:mi><\/mml:msub><mml:mo>,<\/mml:mo><mml:msubsup><mml:mi>s<\/mml:mi><mml:mi>\u03be<\/mml:mi><mml:mo>\u2218<\/mml:mo><\/mml:msubsup><mml:mo>,<\/mml:mo><mml:msubsup><mml:mi>s<\/mml:mi><mml:mi>\u03be<\/mml:mi><mml:mrow><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>c<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:msubsup><\/mml:mrow><\/mml:math>, or<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:msub><mml:mi>l<\/mml:mi><mml:mi>p<\/mml:mi><\/mml:msub><mml:mrow><mml:mo>(<\/mml:mo><mml:mi>\u03be<\/mml:mi><mml:mo>)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>. Then, we give some results on the finite section method for approximating a solution of an infinite linear system. Finally, using a quasi-Newton method, we construct a sequence that converges fast to a solution of an infinite linear system.<\/jats:p>","DOI":"10.1155\/2007\/25704","type":"journal-article","created":{"date-parts":[[2007,7,15]],"date-time":"2007-07-15T07:19:17Z","timestamp":1184483957000},"page":"1-17","source":"Crossref","is-referenced-by-count":0,"title":["Matrix Transformations and Quasi-Newton Methods"],"prefix":"10.1155","volume":"2007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5112-6525","authenticated-orcid":true,"given":"Boubakeur","family":"Benahmed","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruno","family":"de Malafosse","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Adnan","family":"Yassine","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","series-title":"Lecture Notes in Mathematics","volume-title":"Infinite Matrices of Operators","volume":"786","year":"1980"},{"issue":"17","key":"2","first-page":"59","volume":"2003","year":"2003","journal-title":"Filomat"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1155\/S0161171204406498"},{"issue":"3-4","key":"4","first-page":"91","volume":"53","year":"2001","journal-title":"Matematichki Vesnik"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1155\/S0161171203204324"},{"issue":"1-2","key":"6","first-page":"125","volume":"70","year":"2004","journal-title":"Acta Sci. Math Szeged"},{"issue":"1-2","key":"7","first-page":"41","volume":"57","year":"2005","journal-title":"Matematichki Vesnik"},{"issue":"1","key":"8","first-page":"153","volume":"31","year":"1998","journal-title":"Demonstratio Mathematica"},{"issue":"3","key":"9","first-page":"563","volume":"292","year":"1987","journal-title":"Doklady Akademii Nauk SSSR"},{"volume-title":"Infinite Matrices and Sequence Spaces","year":"1950","key":"10"},{"key":"11","series-title":"Research Notes in Mathematics","volume-title":"Algorithmic Methods in Optimal Control","volume":"47","year":"1981"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.2307\/2003239"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1137\/0116055"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01589442"},{"issue":"1","key":"15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0334270000012339","volume":"40","year":"1998","journal-title":"Journal of Australian Mathematical Society. Series B"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1137\/0724045"},{"issue":"1","key":"17","first-page":"25","volume":"9","year":"1985","journal-title":"Journal of Integral Equations"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1137\/0724037"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1137\/0325083"},{"issue":"4","key":"20","first-page":"305","volume":"16","year":"1998","journal-title":"Journal of Computational Mathematics"}],"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2007\/025704.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2007\/025704.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,17]],"date-time":"2017-06-17T16:54:13Z","timestamp":1497718453000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/ijmms\/2007\/025704\/abs\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007]]},"references-count":20,"alternative-id":["025704","25704"],"URL":"https:\/\/doi.org\/10.1155\/2007\/25704","relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2007]]}}}