For those into Numerical Analysis...?

Question

Which one of the following iterative schemes is the best, and why?

i. Newton-Raphson method
ii. Richardson's Fixed Point Iteration method
iii. Jacobi scheme
iv. Gauss-Seidel scheme
v. Successive Over-relaxation scheme (SOR)
vi. Symmetric SOR (SSOR)
vii. Accelerated SOR (ASOR)

Answer 1

Newton-Raphson is the best because it's quadratical converge; Although, the initial points should not be too far from the root, and if the root is near to a singularity point then NR will give false root, Newton-Raphson still the faster and the safe method to find roots for one nonlinear equation or system of nonlinear equations.

Answer 2

between
i. Newton-Raphson method
ii. Richardson's Fixed Point Iteration method
iii. Jacobi scheme
iv. Gauss-Seidel scheme
is:
iii. Jacobi scheme

Answer 3

I prefer Jacobi method because its simple realization for computer worths its inaccuracy for exponential equations.

Answer 4

It depends on the problem you are trying to solve.