Demonstration Of The Ill-Conditioned Nature Of Hilbert Matricies

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)