{"title":"用加性修正法代替旋转法进行LU分解","authors":"Neil Lindquist, P. Luszczek, J. Dongarra","doi":"10.1145/3577193.3593731","DOIUrl":null,"url":null,"abstract":"Direct solvers for dense systems of linear equations commonly use partial pivoting to ensure numerical stability. However, pivoting can introduce significant performance overheads, such as synchronization and data movement, particularly on distributed systems. To improve the performance of these solvers, we present an alternative to pivoting in which numerical stability is obtained through additive updates. We implemented this approach using SLATE, a GPU-accelerated numerical linear algebra library, and evaluated it on the Summit supercomputer. Our approach provides better performance (up to 5-fold speedup) than Gaussian elimination with partial pivoting for comparable accuracy on most of the tested matrices. It also provides better accuracy (up to 15 more digits) than Gaussian elimination with no pivoting for comparable performance.","PeriodicalId":424155,"journal":{"name":"Proceedings of the 37th International Conference on Supercomputing","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Using Additive Modifications in LU Factorization Instead of Pivoting\",\"authors\":\"Neil Lindquist, P. Luszczek, J. Dongarra\",\"doi\":\"10.1145/3577193.3593731\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Direct solvers for dense systems of linear equations commonly use partial pivoting to ensure numerical stability. However, pivoting can introduce significant performance overheads, such as synchronization and data movement, particularly on distributed systems. To improve the performance of these solvers, we present an alternative to pivoting in which numerical stability is obtained through additive updates. We implemented this approach using SLATE, a GPU-accelerated numerical linear algebra library, and evaluated it on the Summit supercomputer. Our approach provides better performance (up to 5-fold speedup) than Gaussian elimination with partial pivoting for comparable accuracy on most of the tested matrices. It also provides better accuracy (up to 15 more digits) than Gaussian elimination with no pivoting for comparable performance.\",\"PeriodicalId\":424155,\"journal\":{\"name\":\"Proceedings of the 37th International Conference on Supercomputing\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-06-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 37th International Conference on Supercomputing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3577193.3593731\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 37th International Conference on Supercomputing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3577193.3593731","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Using Additive Modifications in LU Factorization Instead of Pivoting
Direct solvers for dense systems of linear equations commonly use partial pivoting to ensure numerical stability. However, pivoting can introduce significant performance overheads, such as synchronization and data movement, particularly on distributed systems. To improve the performance of these solvers, we present an alternative to pivoting in which numerical stability is obtained through additive updates. We implemented this approach using SLATE, a GPU-accelerated numerical linear algebra library, and evaluated it on the Summit supercomputer. Our approach provides better performance (up to 5-fold speedup) than Gaussian elimination with partial pivoting for comparable accuracy on most of the tested matrices. It also provides better accuracy (up to 15 more digits) than Gaussian elimination with no pivoting for comparable performance.