{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T04:39:05Z","timestamp":1775018345011,"version":"3.50.1"},"reference-count":17,"publisher":"American Mathematical Society (AMS)","issue":"233","license":[{"start":{"date-parts":[[2000,8,17]],"date-time":"2000-08-17T00:00:00Z","timestamp":966470400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>A two-grid discretization scheme is proposed for solving eigenvalue problems, including both partial differential equations and integral equations. With this new scheme, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a much coarser grid, and the solution of a linear algebraic system on the fine grid and the resulting solution still maintains an asymptotically optimal accuracy.<\/p>","DOI":"10.1090\/s0025-5718-99-01180-1","type":"journal-article","created":{"date-parts":[[2005,7,11]],"date-time":"2005-07-11T21:02:26Z","timestamp":1121115746000},"page":"17-25","source":"Crossref","is-referenced-by-count":199,"title":["A two-grid discretization scheme for eigenvalue problems"],"prefix":"10.1090","volume":"70","author":[{"given":"Jinchao","family":"Xu","sequence":"first","affiliation":[]},{"given":"Aihui","family":"Zhou","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1999,8,17]]},"reference":[{"key":"1","series-title":"Pure and Applied Mathematics, Vol. 65","volume-title":"Sobolev spaces","author":"Adams, Robert A.","year":"1975"},{"issue":"6","key":"2","doi-asserted-by":"publisher","first-page":"2359","DOI":"10.1137\/S0036142993247104","article-title":"A two-level discretization of nonlinear boundary value problems","volume":"33","author":"Axelsson, O.","year":"1996","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"186","key":"3","doi-asserted-by":"publisher","first-page":"275","DOI":"10.2307\/2008468","article-title":"Finite element-Galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems","volume":"52","author":"Babu\u0161ka, I.","year":"1989","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"4","series-title":"Handbook of Numerical Analysis, II","isbn-type":"print","volume-title":"Handbook of numerical analysis. Vol. II","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0444703659"},{"key":"5","series-title":"Computer Science and Applied Mathematics","isbn-type":"print","volume-title":"Spectral approximation of linear operators","author":"Chatelin, Fran\u00e7oise","year":"1983","ISBN":"https:\/\/id.crossref.org\/isbn\/0121706206"},{"key":"6","series-title":"Handbook of Numerical Analysis, II","isbn-type":"print","volume-title":"Handbook of numerical analysis. Vol. II","year":"1991","ISBN":"https:\/\/id.crossref.org\/isbn\/0444703659"},{"key":"7","doi-asserted-by":"publisher","first-page":"191","DOI":"10.1090\/conm\/180\/01971","article-title":"Two-grid methods for mixed finite element approximations of nonlinear parabolic equations","author":"Dawson, Clint N.","year":"1994"},{"issue":"2","key":"8","doi-asserted-by":"publisher","first-page":"435","DOI":"10.1137\/S0036142995293493","article-title":"A two-grid finite difference scheme for nonlinear parabolic equations","volume":"35","author":"Dawson, Clint N.","year":"1998","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"2-3","key":"9","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1016\/0096-3003(94)00134-P","article-title":"Two-level Picard and modified Picard methods for the Navier-Stokes equations","volume":"69","author":"Layton, W.","year":"1995","journal-title":"Appl. Math. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0096-3003","issn-type":"print"},{"issue":"2","key":"10","first-page":"219","article-title":"Some problems concerning approximate solutions of operator equations","volume":"22","author":"Lin, Qun","year":"1979","journal-title":"Acta Math. Sinica","ISSN":"https:\/\/id.crossref.org\/issn\/0583-1431","issn-type":"print"},{"issue":"4","key":"11","doi-asserted-by":"publisher","first-page":"1170","DOI":"10.1137\/0732054","article-title":"Error estimates on a new nonlinear Galerkin method based on two-grid finite elements","volume":"32","author":"Marion, Martine","year":"1995","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"8","key":"12","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1002\/(SICI)1099-0887(199708)13:8<675::AID-CNM98>3.0.CO;2-N","article-title":"Two-grid finite element formulations of the incompressible Navier-Stokes equations","volume":"13","author":"Utnes, T.","year":"1997","journal-title":"Comm. Numer. Methods Engrg.","ISSN":"https:\/\/id.crossref.org\/issn\/1069-8299","issn-type":"print"},{"issue":"2","key":"13","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/0729020","article-title":"A new class of iterative methods for nonselfadjoint or indefinite problems","volume":"29","author":"Xu, Jinchao","year":"1992","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"issue":"4","key":"14","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1137\/1034116","article-title":"Iterative methods by space decomposition and subspace correction","volume":"34","author":"Xu, Jinchao","year":"1992","journal-title":"SIAM Rev.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1445","issn-type":"print"},{"issue":"1","key":"15","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1137\/0915016","article-title":"A novel two-grid method for semilinear elliptic equations","volume":"15","author":"Xu, Jinchao","year":"1994","journal-title":"SIAM J. Sci. Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/1064-8275","issn-type":"print"},{"issue":"5","key":"16","doi-asserted-by":"publisher","first-page":"1759","DOI":"10.1137\/S0036142992232949","article-title":"Two-grid discretization techniques for linear and nonlinear PDEs","volume":"33","author":"Xu, Jinchao","year":"1996","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"17","doi-asserted-by":"crossref","unstructured":"Xu, J. and Zhou, A.(1998): Local and parallel finite element algorithms based on two-grid discretizations, Math. Comp.(to appear).","DOI":"10.1090\/S0025-5718-99-01149-7"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2001-70-233\/S0025-5718-99-01180-1\/S0025-5718-99-01180-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2001-70-233\/S0025-5718-99-01180-1\/S0025-5718-99-01180-1.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T00:21:55Z","timestamp":1627604515000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2001-70-233\/S0025-5718-99-01180-1\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,8,17]]},"references-count":17,"journal-issue":{"issue":"233","published-print":{"date-parts":[[2001,1]]}},"alternative-id":["S0025-5718-99-01180-1"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-99-01180-1","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["0025-5718","1088-6842"],"issn-type":[{"value":"0025-5718","type":"print"},{"value":"1088-6842","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,8,17]]}}}