How do iterative methods compare to other numerical methods?

How do iterative methods compare to other numerical methods?

Iterative methods are often used for solving equations and optimization problems. They can be more efficient than direct methods, especially for large systems.

What are some examples of iterative methods?

Common examples include the Jacobi method, Gauss-Seidel method, and Newton's method. Each has its own advantages depending on the problem.

When should I use iterative methods instead of direct methods?

Use iterative methods when dealing with large, sparse systems or when direct methods are computationally expensive. They can converge faster in these cases.

Are there any drawbacks to using iterative methods?

Yes, iterative methods may not converge for all problems, and their convergence rate can vary. It's important to analyze the specific case.

Can you explain the convergence criteria for these methods?

Convergence criteria often depend on the method used, but generally, it involves checking if the difference between successive approximations is below a certain threshold.