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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Bibliographic Details
Published in: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) pp. 244 - 249
Main Authors: Wang, Junjie, Tian, Min, Wang, Yinglong, He, Guoping, Liu, Tao
Format: Conference Proceeding
Language:English
Published: IEEE 01.12.2022
Subjects:
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
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Summary: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.
DOI:10.1109/HPCC-DSS-SmartCity-DependSys57074.2022.00064