Laboratory for High Performance Scientific Computing and Computer Simulation

Department of Computer Science

University of Kentucky

Lexington, KY 40506-0046, USA

and

Shuting Xu

Department of Computer Information Systems

Virginia State University

Petersburg, VA 23806, USA

Condition number of a matrix is an important measure in numerical analysis and linear algebra. It is a measure of stability or sensitivity of a matrix to numerical operations. However, the direct computation of the condition number of a matrix is very expensive in terms of CPU and memory cost, and becomes prohibitive for large size matrices. We propose to use data mining techniques to estimate the condition number of a given sparse matrix. In particular, we will use Support Vector Machine (SVM) to predict the condition numbers. That is, after computing the sparsity pattern features of a matrix, we use support vector regression (SVR) to predict its condition number. This Online Condition Number Query System (CONQS) allows the users to submit their matrices and to obtain predicted condition numbers for their matrices. The accuracy of our prediction methods may not be as precise as the direct computation methods, but it is much faster. Our online system accepts matrices in Harwell-Boeing (HB) format and in standard MATLAB format. The users can use our system to estimate the condition number of their matrices through LAPACK software as well.

**Mathematics Subject Classification**:

Download the compressed postscript file han2.ps.gz, or the PDF file han2.pdf.

Technical Report 458-06, Department of Computer Science, University of Kentucky, Lexington, KY, 2006.

This research was supported in part by the Kentucky Science and Engineering Foundation under the grant KSEF-148-502-05-132.