Condition number of a matrix is an important measure in numerical
analysis and linear algebra. The general approach to obtaining it is through
direct computation or estimation. The time and memory cost of such
approaches are very high, especially for large size matrices. We propose a
totally different approach to estimating the condition number of a sparse
matrix. That is, after computing the
features of a matrix, we use support vector regression (SVR) to predict
its condition number. We also use feature selection strategies
to further reduce
the response time and improve accuracy. We use a feature
selection criterion which combines the weights from SVR and the
weights from comparison of matrices with their preconditioned counterparts.
Our experiments show that the response time of the prediction method is
on average 15 times faster than the direct
computation approaches, which makes it
suitable for online condition number query.
The accuracy of our prediction
method is not as precise as the general direct computation
methods. However, many people only
care about whether a matrix is well-conditioned or
ill-conditioned or the order of the condition number, not the exact
value of the condition number. For such users,
a rough prediction with quick response time probably is a better choice than
a precise value after waiting for hours or days.