## Grants and Contracts Details

### Description

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.

Status | Finished |
---|---|

Effective start/end date | 5/1/05 → 4/30/07 |

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