KSEF R&D Excellence: Support Vector Machine Approach To Matrix Condition Number Prediction

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. vVe propose to use data mining techniques to predict the condition number of a given sparse matrix. In particular, we will use the Support Vector Machine (SVM) technique to estimate the condition numbers, based on the structural and data features of the matrices. vVe will also develop strategies to select useful features from the extracted matrix features to be used in the prediction process. The final product will be an online condition number query system (OCNQS) for users to submit their matrices and to obtain predicted condition numbers for their matrices. This will be the first step for the PI's team to build an Intelligent Preconditioner Recommendation System (IPRS) to use data mining techniques to facilitate the iterative solution of large sparse linear systems. This is a novel application of data mining techniques in scientific and engineering computing. It is also a completely new approach to estimating the condition number of a matrix. This research project will produce preliminary results for proposals targeting NSF's Program on Science and Engineering Information Integration and Informatics (NSF04-528). Keywords: data mining, feature extraction, support vector machine, matrix, condition number.