{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,28]],"date-time":"2023-12-28T23:29:41Z","timestamp":1703806181260},"reference-count":15,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T00:00:00Z","timestamp":1234310400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Int Trans Operational Res"],"published-print":{"date-parts":[[2009,7]]},"abstract":"Abstract<\/jats:title>Bauschke, Borwein, and Lewis have stated a trichotomy theorem that characterizes when the convergence of the method of alternating projections can be arbitrarily slow. However, there are two errors in their proof of this theorem. In this note, we show that although one of the errors is critical, the theorem itself is correct. We give a different proof that uses the multiplicative form of the spectral theorem, and the theorem holds in any real or complex Hilbert space, not just in a real Hilbert space.<\/jats:p>","DOI":"10.1111\/j.1475-3995.2008.00682.x","type":"journal-article","created":{"date-parts":[[2009,2,11]],"date-time":"2009-02-11T10:12:57Z","timestamp":1234347177000},"page":"413-425","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Characterizing arbitrarily slow convergence in the method of alternating projections"],"prefix":"10.1111","volume":"16","author":[{"given":"Heinz H.","family":"Bauschke","sequence":"first","affiliation":[]},{"given":"Frank","family":"Deutsch","sequence":"additional","affiliation":[]},{"given":"Hein","family":"Hundal","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2009,6,12]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1950-0051437-7"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01027691"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144593251710"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/204\/02620"},{"key":"e_1_2_6_6_1","first-page":"96","volume-title":"Rate of Convergence of the Method of Alternating Projections, ISNM","author":"Deutsch F.","year":"1984"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9298-9"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1997.5202"},{"key":"e_1_2_6_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2006.02.005"},{"key":"e_1_2_6_10_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jat.2006.02.006"},{"key":"e_1_2_6_11_1","unstructured":"Deutsch F. Hundal H. 2008. Characterizing arbitrarily slow convergence for powers of linear operators.SIAM Journal of Optimization forthcoming."},{"key":"e_1_2_6_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(86)90085-5"},{"key":"e_1_2_6_13_1","doi-asserted-by":"publisher","DOI":"10.2307\/2313117"},{"key":"e_1_2_6_14_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02551235"},{"key":"e_1_2_6_15_1","volume-title":"Methods of Modern Mathematical Physics I: Functional Analysis","author":"Reed M.","year":"1972"},{"key":"e_1_2_6_16_1","volume-title":"Functional Operators \u2013 Vol. II. The Geometry of Orthogonal Spaces, Annals of Mathematical Studies #22","author":"Von Neumann J.","year":"1950"}],"container-title":["International Transactions in Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.1475-3995.2008.00682.x","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/j.1475-3995.2008.00682.x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T17:53:01Z","timestamp":1697046781000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/j.1475-3995.2008.00682.x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,6,12]]},"references-count":15,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["10.1111\/j.1475-3995.2008.00682.x"],"URL":"https:\/\/doi.org\/10.1111\/j.1475-3995.2008.00682.x","archive":["Portico"],"relation":{},"ISSN":["0969-6016","1475-3995"],"issn-type":[{"value":"0969-6016","type":"print"},{"value":"1475-3995","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,6,12]]},"assertion":[{"value":"2009-06-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}