An Interim Analysis Report on Preconditioners and Matrices

Shuting Xu, Eun-Joo Lee, and Jun Zhang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA


Preconditioned Krylov subspace methods have become the methods of choice in solving large sparse linear systems. Choosing a good preconditioner for solving a specific sparse linear system is considered the combination of art and science, and requires experience and insight that most application scientists lack. We intend to build an Intelligent Preconditioner Recommendation System, which can provide advice on choosing a high performance preconditioner as well as suitable parameters for a given sparse linear system. In this report, we introduce some of our first results towards this goal. We analyze 319 matrices, each with more than 30 attributes, and their relationships with 6 preconditioners with different parameters.

Key words: Iterative Method, preconditioner, recommendation system, data mining

Mathematics Subject Classification:

Download the compressed postscript file, or the PDF file matrix-mine.pdf.
Technical Report 388-03, Department of Computer Science, University of Kentucky, Lexington, KY, 2003.

The research work of S. Xu and E.-J. Lee was supported in part by the U.S. National Science Foundation under grant ACR-0234270.

The research work of J. Zhang was supported in part by the U.S. National Science Foundation under grants CCR-0092532, and ACR-0202934, and ACR-0234270, by the U.S. Department of Energy Office of Science under grant DE-FG02-02ER45961, by the Kentucky Science & Engineering Foundation under grant KSEF-02-264-RED-002, by the apanese Research Organization for Information Science & Technology, and by the University of Kentucky Research Committee.