In the paper, we consider interval linear algebraic systems of equations Ax = b, with an interval matrix A and interval right-hand side vector b, as a model of imprecise systems of linear algebraic equations of the same form. We propose a new regularization procedure that reduces the solution of the imprecise linear system to computing a point from the tolerable solution set for the interval linear system with a widened right-hand side. The points from the tolerable solution set to the widened interval linear system are called pseudo-solutions, while the best pseudo-solutions are those corresponding to the minimal extension of the right-hand side that produces a nonempty tolerable solution set. We prove the existence of the best pseudo-solutions and propose a method for their computation, as a solution to a linear programming problem. Since the auxiliary linear programming problem may become nearly degenerate, it is necessary to perform computations with a precision that substantially exceeds that of the standard floating point data types. A simplex method with errorless rational computations gives an effective solution to the problem. Coarse-grained parallelism for distributed computer systems using MPI and the software for errorless rational calculations using CUDA C small-grained parallelism are the main instruments of our suitable implementation.<\/p>\n","protected":false},"excerpt":{"rendered":"
In the paper, we consider interval linear algebraic systems of equations Ax = b, with an interval matrix A and interval right-hand side vector b, as a model of imprecise systems of linear algebraic equations of the same form. We propose a new regularization procedure that reduces the solution of the imprecise linear system to […]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[11,89,3],"tags":[1782,14,37,242,20,1015],"class_list":["post-11296","post","type-post","status-publish","format-standard","hentry","category-computer-science","category-nvidia-cuda","category-paper","tag-computer-science","tag-cuda","tag-linear-algebra","tag-mpi","tag-nvidia","tag-nvidia-geforce-gtx-460"],"views":1996,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/11296","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/users\/351"}],"replies":[{"embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=11296"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/11296\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=11296"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=11296"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=11296"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}