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)