TY - JOUR
T1 - An Empirical Analysis of the Performance of Preconditioners for SPD Systems
AU - George, Thomas
AU - Gupta, Anshul
AU - Sarin, Vivek
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: This work was partly supported by Award No. KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2012/8/1
Y1 - 2012/8/1
N2 - Preconditioned iterative solvers have the potential to solve very large sparse linear systems with a fraction of the memory used by direct methods. However, the effectiveness and performance of most preconditioners is not only problem dependent, but also fairly sensitive to the choice of their tunable parameters. As a result, a typical practitioner is faced with an overwhelming number of choices of solvers, preconditioners, and their parameters. The diversity of preconditioners makes it difficult to analyze them in a unified theoretical model. A systematic empirical evaluation of existing preconditioned iterative solvers can help in identifying the relative advantages of various implementations. We present the results of a comprehensive experimental study of the most popular preconditioner and iterative solver combinations for symmetric positive-definite systems. We introduce a methodology for a rigorous comparative evaluation of various preconditioners, including the use of some simple but powerful metrics. The detailed comparison of various preconditioner implementations and a state-of-the-art direct solver gives interesting insights into their relative strengths and weaknesses. We believe that these results would be useful to researchers developing preconditioners and iterative solvers as well as practitioners looking for appropriate sparse solvers for their applications. © 2012 ACM.
AB - Preconditioned iterative solvers have the potential to solve very large sparse linear systems with a fraction of the memory used by direct methods. However, the effectiveness and performance of most preconditioners is not only problem dependent, but also fairly sensitive to the choice of their tunable parameters. As a result, a typical practitioner is faced with an overwhelming number of choices of solvers, preconditioners, and their parameters. The diversity of preconditioners makes it difficult to analyze them in a unified theoretical model. A systematic empirical evaluation of existing preconditioned iterative solvers can help in identifying the relative advantages of various implementations. We present the results of a comprehensive experimental study of the most popular preconditioner and iterative solver combinations for symmetric positive-definite systems. We introduce a methodology for a rigorous comparative evaluation of various preconditioners, including the use of some simple but powerful metrics. The detailed comparison of various preconditioner implementations and a state-of-the-art direct solver gives interesting insights into their relative strengths and weaknesses. We believe that these results would be useful to researchers developing preconditioners and iterative solvers as well as practitioners looking for appropriate sparse solvers for their applications. © 2012 ACM.
UR - http://hdl.handle.net/10754/597521
UR - https://dl.acm.org/doi/10.1145/2331130.2331132
UR - http://www.scopus.com/inward/record.url?scp=84866516596&partnerID=8YFLogxK
U2 - 10.1145/2331130.2331132
DO - 10.1145/2331130.2331132
M3 - Article
SN - 0098-3500
VL - 38
SP - 1
EP - 30
JO - ACM Transactions on Mathematical Software
JF - ACM Transactions on Mathematical Software
IS - 4
ER -