What are the differences between iterative methods and direct methods in numerical analysis?

What are the differences between iterative methods and direct methods in numerical analysis?

Iterative methods solve problems by refining an initial guess through repeated approximations, while direct methods compute the solution in a finite number of steps.

Can you give me examples of each method?

Sure! An example of an iterative method is the Jacobi method, and a direct method example is Gaussian elimination.

When should I use one method over the other?

Use iterative methods for large systems where direct methods may be computationally expensive, and direct methods for smaller, well-conditioned problems.

Are there any drawbacks to using iterative methods?

Yes, iterative methods may converge slowly or fail to converge if the initial guess is not close enough to the actual solution.