NDLI: Revisiting Asynchronous Linear Solvers: Provable Convergence Rate through Randomization

Content Provider	ACM Digital Library
Author	Avron, Haim Druinsky, Alex Gupta, Anshul
Copyright Year	2015
Abstract	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. 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. 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.
Starting Page	1
Ending Page	27
Page Count	27
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/2814566
Journal	Journal of the ACM (JACM)
Volume Number	62
Issue Number	6
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2015-12-10
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Asynchronous Gauss-Seidel Randomized Shared-memory parallel
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Revisiting Asynchronous Linear Solvers: Provable Convergence Rate through Randomization

Revisiting asynchronous linear solvers: Provable convergence rate through randomization. IPDPS (2014)

Parameterized Verification of Asynchronous Shared-Memory Systems

Revisiting Asynchronous Linear Solvers: Provable Convergence Rate Through Randomization

On Stable Parallel Linear System Solvers

Tight bounds for asynchronous randomized consensus

Correctness properties in a shared-memory parallel language

Parallel hashing: an efficient implementation of shared memory

Fault-tolerant wait-free shared objects

Revisiting Asynchronous Linear Solvers: Provable Convergence Rate through Randomization

Similar Documents

Revisiting Asynchronous Linear Solvers: Provable Convergence Rate through Randomization

Revisiting asynchronous linear solvers: Provable convergence rate through randomization. IPDPS (2014)

Parameterized Verification of Asynchronous Shared-Memory Systems

Revisiting Asynchronous Linear Solvers: Provable Convergence Rate Through Randomization

On Stable Parallel Linear System Solvers

Tight bounds for asynchronous randomized consensus

Correctness properties in a shared-memory parallel language

Parallel hashing: an efficient implementation of shared memory

Fault-tolerant wait-free shared objects

Revisiting Asynchronous Linear Solvers: Provable Convergence Rate through Randomization