What are the main challenges of iterative methods in numerical analysis?

What are the main challenges of iterative methods in numerical analysis?

Iterative methods can face several challenges, including convergence issues, sensitivity to initial guesses, and computational cost.

Can you explain what convergence issues mean?

Convergence issues refer to the difficulty in ensuring that an iterative method approaches the correct solution as iterations progress.

What factors affect the convergence of these methods?

Factors include the choice of initial guess, the nature of the function, and the method's inherent stability.

Are there specific iterative methods that are more prone to these challenges?

Yes, methods like the Newton-Raphson can struggle with convergence if the initial guess is far from the actual root.

How can these challenges be mitigated?

Challenges can be mitigated by using better initial guesses, employing convergence acceleration techniques, and analyzing the problem's structure.