What are the limitations of iteration methods in numerical analysis?

What are the limitations of iteration methods in numerical analysis?

Iteration methods are powerful, but they can have limitations such as convergence issues, sensitivity to initial guesses, and computational cost.

Can you explain what convergence issues mean?

Convergence issues refer to the failure of an iterative method to approach a solution, which can happen if the method is not well-suited for the problem.

What factors affect the convergence of these methods?

Factors include the choice of initial guess, the nature of the function, and the specific algorithm used for iteration.

Are there any specific examples of problems where iteration methods fail?

Yes, problems with discontinuities or steep gradients can lead to failure in convergence for many iteration methods.

How can I improve the performance of iteration methods?

You can improve performance by refining your initial guess, using more robust algorithms, or applying techniques like relaxation.