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We also show that our preconditioners fit into the additive Schwarz framework with appropriately chosen subspace decompositions. Condition numbers associated with the new algorithms are computed numerically in several cases and compared with those of the corresponding algorithms in which exact subdomain solves are used.<\/p>","DOI":"10.1090\/s0025-5718-98-00879-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"1-19","source":"Crossref","is-referenced-by-count":18,"title":["Analysis of non-overlapping domain decomposition algorithms with inexact solves"],"prefix":"10.1090","volume":"67","author":[{"given":"James","family":"Bramble","sequence":"first","affiliation":[]},{"given":"Joseph","family":"Pasciak","sequence":"additional","affiliation":[]},{"given":"Apostol","family":"Vassilev","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"6","key":"1","doi-asserted-by":"publisher","first-page":"1097","DOI":"10.1137\/0723075","article-title":"Iterative methods for the solution of elliptic problems on regions partitioned into substructures","volume":"23","author":"Bj\u00f8rstad, Petter E.","year":"1986","journal-title":"SIAM J. 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