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)