{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T21:53:46Z","timestamp":1780350826991,"version":"3.54.1"},"reference-count":23,"publisher":"American Mathematical Society (AMS)","issue":"275","license":[{"start":{"date-parts":[[2012,2,18]],"date-time":"2012-02-18T00:00:00Z","timestamp":1329523200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>This paper provides a new two-grid discretization method for solving partial differential equation or integral equation eigenvalue problems. In 2001, Xu and Zhou introduced a scheme that reduces the solution of an eigenvalue problem on a finite element grid to that of one single linear problem on the same grid together with a similar eigenvalue problem on a much coarser grid. By solving a slightly different linear problem on the fine grid, the new algorithm in this paper significantly improves the theoretical error estimate which allows a much coarser mesh to achieve the same asymptotic convergence rate. Numerical examples are also provided to demonstrate the efficiency of the new method.<\/p>","DOI":"10.1090\/s0025-5718-2011-02458-0","type":"journal-article","created":{"date-parts":[[2011,2,18]],"date-time":"2011-02-18T09:43:41Z","timestamp":1298022221000},"page":"1287-1301","source":"Crossref","is-referenced-by-count":60,"title":["Acceleration of a two-grid method for eigenvalue problems"],"prefix":"10.1090","volume":"80","author":[{"given":"Xiaozhe","family":"Hu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xiaoliang","family":"Cheng","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2011,2,18]]},"reference":[{"issue":"6","key":"1","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. 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