{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T03:01:07Z","timestamp":1785985267473,"version":"3.56.0"},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013,10,1]]},"abstract":"<jats:title>Abstract.<\/jats:title><jats:p>\nWe present some new error estimates for the eigenvalues and\neigenfunctions obtained by the Rayleigh\u2013Ritz method, the common\nvariational method to solve eigenproblems. The errors are bounded\nin terms of the error of the best approximation of the\neigenfunction under consideration by functions in the ansatz space.\nIn contrast to the classical theory, the approximation error of\neigenfunctions other than the given one does not enter into these\nestimates. The estimates are based on a bound for the norm of a\ncertain projection operator, e.g., in finite element methods for\nsecond order eigenvalue problems, the <jats:italic>H<jats:sup>1<\/jats:sup><\/jats:italic>-norm of the\n<jats:italic>L<jats:sub>2<\/jats:sub><\/jats:italic>-projection onto the finite element space.\n<\/jats:p>","DOI":"10.1515\/cmam-2013-0013","type":"journal-article","created":{"date-parts":[[2013,10,1]],"date-time":"2013-10-01T02:31:54Z","timestamp":1380594714000},"page":"495-502","source":"Crossref","is-referenced-by-count":21,"title":["A Short Theory of the Rayleigh\u2013Ritz Method"],"prefix":"10.1515","volume":"13","author":[{"given":"Harry","family":"Yserentant","sequence":"first","affiliation":[{"name":"1Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, 10623 Berlin, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"374","container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/13\/4\/article-p495.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/downloadpdf\/journals\/cmam\/13\/4\/article-p495.xml","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,28]],"date-time":"2021-02-28T03:03:43Z","timestamp":1614481423000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2013-0013\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,10,1]]},"references-count":0,"journal-issue":{"issue":"4"},"URL":"https:\/\/doi.org\/10.1515\/cmam-2013-0013","relation":{},"ISSN":["1609-4840","1609-9389"],"issn-type":[{"value":"1609-4840","type":"print"},{"value":"1609-9389","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,10,1]]}}}