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For the sake of portability, simplicity, flexibility, and efficiency, the FGMRES solvers have been implemented in Fortran 77 using the reverse communication mechanism for the matrix-vector product, the preconditioning, and the dot-product computations. For distributed-memory computation, several orthogonalization procedures have been implemented to reduce the cost of the dot-product calculation, which is a well-known bottleneck of efficiency for Krylov methods. Furthermore, either implicit or explicit calculation of the residual at restart is possible depending on the actual cost of the matrix-vector product. Finally, the implemented stopping criterion is based on a normwise backward error.<\/jats:p>","DOI":"10.1145\/1377612.1377617","type":"journal-article","created":{"date-parts":[[2008,7,29]],"date-time":"2008-07-29T13:22:19Z","timestamp":1217337739000},"page":"1-12","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Algorithm 881"],"prefix":"10.1145","volume":"35","author":[{"given":"Val\u00e9rie","family":"Frayss\u00e9","sequence":"first","affiliation":[{"name":"Kvasar Technology LLC"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luc","family":"Giraud","sequence":"additional","affiliation":[{"name":"ENSEEIHT-IRIT"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Serge","family":"Gratton","sequence":"additional","affiliation":[{"name":"CNES"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2008,7]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Tech. 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