We present a multi-stage method for solving large tridiagonal systems on the GPU. Previously large tridiagonal systems cannot be efficiently solved due to the limitation of on-chip shared memory size. We tackle this problem by splitting the systems into smaller ones and then solving them on-chip. The multi-stage characteristic of our method, together with various workloads and GPUs of different capabilities, obligates an auto-tuning strategy to carefully select the switch points between computation stages. In particular, we show two ways to effectively prune the tuning space and thus avoid an impractical exhaustive search: (1) apply algorithmic knowledge to decouple tuning parameters, and (2) estimate search starting points based on GPU architecture parameters. We demonstrate that auto-tuning is a powerful tool that improves the performance by up to 5x, saves 17% and 32% of execution time on average respectively over static and dynamic tuning, and enables our multi-stage solver to outperform the Intel MKL tridiagonal solver on many parallel tridiagonal systems by 6-11x.<\/p>\n","protected":false},"excerpt":{"rendered":"
We present a multi-stage method for solving large tridiagonal systems on the GPU. Previously large tridiagonal systems cannot be efficiently solved due to the limitation of on-chip shared memory size. We tackle this problem by splitting the systems into smaller ones and then solving them on-chip. The multi-stage characteristic of our method, together with various […]<\/p>\n","protected":false},"author":351,"featured_media":0,"comment_status":"open","ping_status":"open","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":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[36,11,89,3],"tags":[1787,1782,14,37,20,183,234,953],"class_list":["post-5917","post","type-post","status-publish","format-standard","hentry","category-algorithms","category-computer-science","category-nvidia-cuda","category-paper","tag-algorithms","tag-computer-science","tag-cuda","tag-linear-algebra","tag-nvidia","tag-nvidia-geforce-8800-gtx","tag-nvidia-geforce-gtx-280","tag-nvidia-geforce-gtx-470"],"views":2146,"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/5917","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=5917"}],"version-history":[{"count":0,"href":"https:\/\/hgpu.org\/index.php?rest_route=\/wp\/v2\/posts\/5917\/revisions"}],"wp:attachment":[{"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5917"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5917"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/hgpu.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5917"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}