PRKP: A Parallel Randomized Iterative Algorithm for Solving Linear Systems
This paper proposes a distributed-memory parallel randomized iterative algorithm for solving linear systems, called the parallel randomized kaczmarz projection (PRKP) algorithm. The algorithm has the property of greedy sampling, alternating projection, and lazy approximation. We derive the alternati...
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| Vydané v: | 2022 IEEE 24th Int Conf on High Performance Computing & Communications; 8th Int Conf on Data Science & Systems; 20th Int Conf on Smart City; 8th Int Conf on Dependability in Sensor, Cloud & Big Data Systems & Application (HPCC/DSS/SmartCity/DependSys) s. 244 - 249 |
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01.12.2022
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| Abstract | This paper proposes a distributed-memory parallel randomized iterative algorithm for solving linear systems, called the parallel randomized kaczmarz projection (PRKP) algorithm. The algorithm has the property of greedy sampling, alternating projection, and lazy approximation. We derive the alternating projection process from the Randomized Kaczmarz algorithm and develop the greedy sampling and lazy approximation process to improve the convergence rate and reduce the per-process communication volume. Moreover, we develop a sampling residual estimation scheme for our proposed algorithm, which greatly reduces the extra computation cost required to obtain residuals. Our experimental results show that the proposed algorithm significantly outperforms previous parallel iterative algorithms on overdetermined linear systems, and yields up to \mathbf{159}\times and \mathbf{384}\times speedups on average respectively compared to the leading pipelined CG and pipelined GMRES algorithms. |
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| AbstractList | This paper proposes a distributed-memory parallel randomized iterative algorithm for solving linear systems, called the parallel randomized kaczmarz projection (PRKP) algorithm. The algorithm has the property of greedy sampling, alternating projection, and lazy approximation. We derive the alternating projection process from the Randomized Kaczmarz algorithm and develop the greedy sampling and lazy approximation process to improve the convergence rate and reduce the per-process communication volume. Moreover, we develop a sampling residual estimation scheme for our proposed algorithm, which greatly reduces the extra computation cost required to obtain residuals. Our experimental results show that the proposed algorithm significantly outperforms previous parallel iterative algorithms on overdetermined linear systems, and yields up to \mathbf{159}\times and \mathbf{384}\times speedups on average respectively compared to the leading pipelined CG and pipelined GMRES algorithms. |
| Author | Tian, Min Wang, Yinglong He, Guoping Liu, Tao Wang, Junjie |
| Author_xml | – sequence: 1 givenname: Junjie surname: Wang fullname: Wang, Junjie email: 10431200760@stu.qlu.edu.cn organization: School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences),Jinan,China – sequence: 2 givenname: Min surname: Tian fullname: Tian, Min email: tianm@sdas.org organization: Qilu University of Technology (Shandong Academy of Sciences),Shandong Computer Science Center (National Supercomputer Center in Jinan),Jinan,China – sequence: 3 givenname: Yinglong surname: Wang fullname: Wang, Yinglong email: wangyl@sdas.org organization: Qilu University of Technology (Shandong Academy of Sciences),Shandong Computer Science Center (National Supercomputer Center in Jinan),Jinan,China – sequence: 4 givenname: Guoping surname: He fullname: He, Guoping email: hegp@sdas.org organization: Qilu University of Technology (Shandong Academy of Sciences),Shandong Computer Science Center (National Supercomputer Center in Jinan),Jinan,China – sequence: 5 givenname: Tao surname: Liu fullname: Liu, Tao email: liutao@sdas.org organization: Qilu University of Technology (Shandong Academy of Sciences),Shandong Computer Science Center (National Supercomputer Center in Jinan),Jinan,China |
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| PublicationTitle | 2022 IEEE 24th Int Conf on High Performance Computing & Communications; 8th Int Conf on Data Science & Systems; 20th Int Conf on Smart City; 8th Int Conf on Dependability in Sensor, Cloud & Big Data Systems & Application (HPCC/DSS/SmartCity/DependSys) |
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| Snippet | This paper proposes a distributed-memory parallel randomized iterative algorithm for solving linear systems, called the parallel randomized kaczmarz projection... |
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| StartPage | 244 |
| SubjectTerms | alternating projection Approximation algorithms Costs distributed memory systems Estimation Iterative algorithms Linear systems overdetermined linear systems parallel algorithms parallel iterative methods Processor scheduling randomized projection Scheduling |
| Title | PRKP: A Parallel Randomized Iterative Algorithm for Solving Linear Systems |
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