There are several commonly used iterative methods in numerical computations. Here are a few examples:

  1. The Newton-Raphson method: This method is used to find the root of a nonlinear equation. It requires the function and its derivative as inputs and it uses successive approximations to converge to the root. The method is based on linearizing the function at each iteration.

  2. The Jacobi method: This method is used to solve systems of linear equations. It involves splitting the matrix into a diagonal component and off-diagonal components. At each iteration, the solution is updated using the diagonal components and the previous iteration's solution. The method is known for its simplicity but it can be slow to converge.

  3. The Gauss-Seidel method: This method is also used to solve systems of linear equations. It is similar to the Jacobi method but at each iteration, it uses the most up-to-date approximations of the solution for updating. This can lead to faster convergence compared to the Jacobi method.

  4. The Successive Overrelaxation (SOR) method: This method is a modification of the Gauss-Seidel method. It introduces a relaxation factor that can accelerate convergence. By properly choosing the relaxation factor, the SOR method can sometimes converge faster than the Gauss-Seidel method.

  5. The Conjugate Gradient method: This method is used to solve large systems of linear equations where the matrix is symmetric and positive definite. It is an iterative method that iteratively seeks a solution in a subspace spanned by the residual vectors. The method can converge quickly for certain types of matrices.

  These are just a few examples of commonly used iterative methods in numerical computations. The choice of method depends on the problem at hand, the available computational resources, and the desired level of accuracy.