What are the convergence criteria in iterative methods?

What are the convergence criteria in iterative methods?

Convergence criteria in iterative methods determine when an algorithm can stop iterating. Common criteria include a small enough error tolerance or a maximum number of iterations.

Can you explain the difference between absolute and relative error?

Absolutely! Absolute error measures the difference between the exact value and the approximation, while relative error compares the absolute error to the exact value, providing a sense of scale.

How do these criteria affect the performance of iterative methods?

These criteria directly impact performance; stricter criteria may lead to more iterations and longer computation times, while looser criteria can result in faster convergence but less accuracy.

What are some common iterative methods used in practice?

Common iterative methods include the Jacobi method, Gauss-Seidel method, and Newton's method, each with its own convergence characteristics.