What are the limitations of iterative methods in numerical analysis?

What are the limitations of iterative methods in numerical analysis?

Iterative methods can be limited by convergence issues, sensitivity to initial guesses, and computational cost.

Can you explain what convergence issues mean?

Convergence issues refer to the method's inability to approach a solution, which can happen if the method diverges.

How does the initial guess affect the outcome?

The initial guess can significantly impact convergence; a poor choice may lead to slow convergence or divergence.

Are there specific problems where iterative methods fail?

Yes, problems with discontinuities or non-linearities can cause iterative methods to fail or perform poorly.

What alternatives exist if iterative methods are not suitable?

Alternatives include direct methods like Gaussian elimination or using hybrid approaches that combine both methods.