An Empirical Analysis of Iterative Solver Performance for SPD Systems

Direct methods for solving sparse systems of linear equations are fast and robust, but can consume an impractical amount of memory, particularly for large three-dimensional problems. Preconditioned iterative solvers have the potential to solve very large systems with a fraction of the memory used by direct methods. The diversity of preconditioners makes it difficult to analyze them in a unified theoretical model. hence, a systematic evaluation of existing preconditioned iterative solvers is necessary to identify the relative advantages of iterative methods and to guide future efforts. We present the results of a comprehensive experimental study of the most popular preconditioner and iterative solver combinations for symmetric positive-definite systems. A detailed comparison of the preconditioners, the iterative solver packages, and a state-of-the-are direct solver gives interesting insights into their 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.

By: Thomas George; Anshul Gupta; Vivek Sarin

Published in: RC24737 in 2009


This Research Report is available. This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Report for early dissemination of its contents. In view of the transfer of copyright to the outside publisher, its distribution outside of IBM prior to publication should be limited to peer communications and specific requests. After outside publication, requests should be filled only by reprints or legally obtained copies of the article (e.g., payment of royalties). I have read and understand this notice and am a member of the scientific community outside or inside of IBM seeking a single copy only.


Questions about this service can be mailed to .