What are the conditions when we use direct and iterative methods? What are the drawbacks of direct methods of solution of linear equations?

We use direct methods in absence of round off errors. Such method would yield the exact soluton within finite number of steps.

It is useful for problems involving special, very large matrices.

In time dependent problems, direct method can not make good use of such information.
Sometime only matrix vector products are given. In other words, the matrix is not available explicitly or is very expensive to computer for example in DSP (Digital Signal Processing)

Computer Science and Information Technology