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This paper deals with a new class of parallel asynchronous iterative algorithms for the solution of nonlinear systems of equations. The main feature of the new class of methods presented here is the possibility of flexible communication between processors. In particular partial updates can be exchanged. Approximation of the associated fixed point mapping is also considered. A detailed convergence study is presented. A connection with the Schwarz alternating method is made for the solution of nonlinear boundary value problems. Computational results on a shared memory multiprocessor IBM 3090 are briefly presented.<\/p>","DOI":"10.1090\/s0025-5718-98-00885-0","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T22:14:44Z","timestamp":1027721684000},"page":"237-255","source":"Crossref","is-referenced-by-count":42,"title":["A new class of asynchronous iterative algorithms with order intervals"],"prefix":"10.1090","volume":"67","author":[{"given":"J.","family":"Miellou","sequence":"first","affiliation":[]},{"given":"D.","family":"El Baz","sequence":"additional","affiliation":[]},{"given":"P.","family":"Spiteri","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"issue":"5","key":"1","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1016\/0167-8191(93)90003-4","article-title":"Contractive mappings with maximum norms: comparison of constants of contraction and application to asynchronous iterations","volume":"19","author":"Bahi, M.","year":"1993","journal-title":"Parallel Comput.","ISSN":"http:\/\/id.crossref.org\/issn\/0167-8191","issn-type":"print"},{"key":"2","doi-asserted-by":"crossref","unstructured":"R. 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