### Demonstration Of The Ill-Conditioned Nature Of Hilbert Matricies

## An application of numerical analysis techniques

In this assignment I used LU decomposition to solve
the matrix equation `H . X = B`

where `H`

corresponds to
a Hilbert matrix of order `n`

, and all elements of `B`

are
unity, and compare these results with those given by
more accurate integer methods. I found that while the
error from the LU decomposition increase
exponentially with `n`

, the routine still coped very well
with quite extremely ill-conditioned matrices over the
range of `n`

used (`2`

to `10`

). However, for
characteristically ill-conditioned matrix systems, one
should generally endeavour to find analytical solutions
as opposed to utilising numerical methods when
accuracy is of primary importance.

An application of LU-decomposition. (3rd Year)