{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T21:50:57Z","timestamp":1649022657305},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2013,6]]},"abstract":"<jats:p> In this paper, we introduce a geometric model for linear symmetric eigenvalue problem, which is motivated by the fact that any eigenvalue of a symmetric positive definite matrix A is the reciprocal of the square length of an axis of the ellipsoid x<jats:sup>T<\/jats:sup>Ax = 1. Hence, to find the largest eigenvalue is equivalent to calculate the shortest axis of the corresponding ellipsoid. Two sequential subspace projection algorithms based on this idea are proposed, and we establish the global convergence and local linear convergence rate of our proposed algorithms. Numerical experiments demonstrate that our algorithm outperforms the MATLAB built-in solver \"EIGS\" which calls the famous package \"ARPACK\". <\/jats:p>","DOI":"10.1142\/s0217595913400034","type":"journal-article","created":{"date-parts":[[2013,6,27]],"date-time":"2013-06-27T02:06:26Z","timestamp":1372298786000},"page":"1340003","source":"Crossref","is-referenced-by-count":1,"title":["A SEQUENTIAL SUBSPACE PROJECTION METHOD FOR LINEAR SYMMETRIC EIGENVALUE PROBLEM"],"prefix":"10.1142","volume":"30","author":[{"given":"XIN","family":"LIU","sequence":"first","affiliation":[{"name":"State Key Laboratory of Scientific and Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CHUNLIN","family":"HAO","sequence":"additional","affiliation":[{"name":"Beijing University of Technology, Beijing 100124, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MINGHOU","family":"CHENG","sequence":"additional","affiliation":[{"name":"Huada Empyrean Software Co., Ltd., Beijing 100102, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2013,6,26]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501397949"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1137\/040613305"},{"key":"rf4","first-page":"1","volume":"38","author":"Davis T. A.","year":"2011","journal-title":"ACM Transactions on Mathematical Software"},{"key":"rf5","volume-title":"Matrix Computaion","author":"Golub G. H.","year":"2011"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00413-1"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(96)00238-8"},{"key":"rf9","series-title":"Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods","volume-title":"ARPACK User's Guide","author":"Lehoucq R.","year":"1997"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1002\/nla.246"},{"key":"rf11","volume-title":"Numerical Methods for Large Eigenvalue Problems: Theory and Algorithms","author":"Saad Y.","year":"1992"},{"key":"rf13","volume-title":"The Algebraic Eigenvalue Problem","author":"Wilkinson J. H.","year":"1965"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1142\/9789812709356_0012"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595913400034","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:32:46Z","timestamp":1565116366000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0217595913400034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,6]]},"references-count":11,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2013,6,26]]},"published-print":{"date-parts":[[2013,6]]}},"alternative-id":["10.1142\/S0217595913400034"],"URL":"https:\/\/doi.org\/10.1142\/s0217595913400034","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"value":"0217-5959","type":"print"},{"value":"1793-7019","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,6]]}}}