{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T12:18:04Z","timestamp":1763468284585,"version":"3.41.0"},"reference-count":20,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2015,12,10]],"date-time":"2015-12-10T00:00:00Z","timestamp":1449705600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"name":"XDATA program of the Defense Advanced Research Projects Agency (DARPA), administered through Air Force Research Laboratory","award":["FA8750-12-C-0323"],"award-info":[{"award-number":["FA8750-12-C-0323"]}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["J. ACM"],"published-print":{"date-parts":[[2015,12,10]]},"abstract":"<jats:p>Asynchronous methods for solving systems of linear equations have been researched since Chazan and Miranker's [1969] pioneering paper on chaotic relaxation. The underlying idea of asynchronous methods is to avoid processor idle time by allowing the processors to continue to make progress even if not all progress made by other processors has been communicated to them.<\/jats:p>\n          <jats:p>Historically, the applicability of asynchronous methods for solving linear equations has been limited to certain restricted classes of matrices, such as diagonally dominant matrices. Furthermore, analysis of these methods focused on proving convergence in the limit. Comparison of the asynchronous convergence rate with its synchronous counterpart and its scaling with the number of processors have seldom been studied and are still not well understood.<\/jats:p>\n          <jats:p>In this article, we propose a randomized shared-memory asynchronous method for general symmetric positive definite matrices. We rigorously analyze the convergence rate and prove that it is linear and is close to that of the method's synchronous counterpart if the processor count is not excessive relative to the size and sparsity of the matrix. We also present an algorithm for unsymmetric systems and overdetermined least-squares. Our work presents a significant improvement in the applicability of asynchronous linear solvers as well as in their convergence analysis, and suggests randomization as a key paradigm to serve as a foundation for asynchronous methods.<\/jats:p>","DOI":"10.1145\/2814566","type":"journal-article","created":{"date-parts":[[2015,12,14]],"date-time":"2015-12-14T14:19:41Z","timestamp":1450102781000},"page":"1-27","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":29,"title":["Revisiting Asynchronous Linear Solvers"],"prefix":"10.1145","volume":"62","author":[{"given":"Haim","family":"Avron","sequence":"first","affiliation":[{"name":"IBM T. J. Watson Research Center, Yorktown Heights, NY"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alex","family":"Druinsky","sequence":"additional","affiliation":[{"name":"IBM T. J. Watson Research Center, Yorktown Heights, NY"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anshul","family":"Gupta","sequence":"additional","affiliation":[{"name":"IBM T. J. Watson Research Center, Yorktown Heights, NY"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,12,10]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1109\/IPDPS.2014.31"},{"key":"e_1_2_1_2_1","unstructured":"H. Avron A. Druinsky and S. Toledo. 2013. Reliable iterative condition-number estimation. CoRR abs\/1301.1107 (2013). http:\/\/arxiv.org\/abs\/1301.1107.  H. Avron A. Druinsky and S. Toledo. 2013. Reliable iterative condition-number estimation. CoRR abs\/1301.1107 (2013). http:\/\/arxiv.org\/abs\/1301.1107."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/322063.322067"},{"key":"e_1_2_1_4_1","unstructured":"D. P. Bertsekas and J. N. Tsitsiklis. 1989. 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In Proceedings of the IEEE Conference on Decision and Control. N. M. Freris and A. Zouzias. 2012. Fast distributed smoothing for network clock synchronization. In Proceedings of the IEEE Conference on Decision and Control."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-0427(00)00409-X"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2012.04.052"},{"key":"e_1_2_1_10_1","unstructured":"J. Hook and N. J. Dingle. 2013. Performance analysis of asynchronous parallel Jacobi. MIMS EPrint 2013.52 University of Manchester 27 pages.  J. Hook and N. J. Dingle. 2013. Performance analysis of asynchronous parallel Jacobi. MIMS EPrint 2013.52 University of Manchester 27 pages."},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.1100.0456"},{"key":"e_1_2_1_12_1","first-page":"1","article-title":"Asynchronous stochastic coordinate descent: Parallelism and convergence properties","volume":"25","author":"Liu J.","year":"2014","unstructured":"J. Liu and S. J. Wright . 2014 . Asynchronous stochastic coordinate descent: Parallelism and convergence properties . SIAM J. Optim. 25 , 1 . J. Liu and S. J. Wright. 2014. Asynchronous stochastic coordinate descent: Parallelism and convergence properties. SIAM J. Optim. 25, 1.","journal-title":"SIAM J. Optim."},{"volume-title":"Proceedings of the International Conference in Machine Learning (ICML).","author":"Liu J.","key":"e_1_2_1_13_1","unstructured":"J. Liu , S. J. Wright , C. Re , V. Bittorf , and S. Sridhar . 2014a. An asynchronous parallel stochastic coordinate descent algorithm . In Proceedings of the International Conference in Machine Learning (ICML). J. Liu, S. J. Wright, C. Re, V. Bittorf, and S. Sridhar. 2014a. An asynchronous parallel stochastic coordinate descent algorithm. In Proceedings of the International Conference in Machine Learning (ICML)."},{"key":"e_1_2_1_14_1","unstructured":"J. Liu S. J. Wright and S. Sridhar. 2014b. An asynchronous parallel randomized Kaczmarz algorithm. arxiv: 1401. 4780.  J. Liu S. J. Wright and S. Sridhar. 2014b. An asynchronous parallel randomized Kaczmarz algorithm. arxiv: 1401. 4780."},{"volume-title":"Proceedings of the 24th Advances in Neural Information Processing Systems (NIPS). 693--701","author":"Niu F.","key":"e_1_2_1_15_1","unstructured":"F. Niu , B. Recht , C. Re , and S. J. Wright . 2011. Hogwild: A lock-free approach to parallelizing stochastic gradient descent . In Proceedings of the 24th Advances in Neural Information Processing Systems (NIPS). 693--701 . F. Niu, B. Recht, C. Re, and S. J. Wright. 2011. Hogwild: A lock-free approach to parallelizing stochastic gradient descent. In Proceedings of the 24th Advances in Neural Information Processing Systems (NIPS). 693--701."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599362314"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1137\/0914028"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1145\/2063384.2063405"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902401074"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00041-008-9030-4"}],"container-title":["Journal of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2814566","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2814566","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T05:48:42Z","timestamp":1750225722000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2814566"}},"subtitle":["Provable Convergence Rate through Randomization"],"short-title":[],"issued":{"date-parts":[[2015,12,10]]},"references-count":20,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2015,12,10]]}},"alternative-id":["10.1145\/2814566"],"URL":"https:\/\/doi.org\/10.1145\/2814566","relation":{},"ISSN":["0004-5411","1557-735X"],"issn-type":[{"type":"print","value":"0004-5411"},{"type":"electronic","value":"1557-735X"}],"subject":[],"published":{"date-parts":[[2015,12,10]]},"assertion":[{"value":"2014-07-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-08-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2015-12-10","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}