Question

Write stopping rules to obtain approximate solution for given non-linear equation

Answer 1

Answer:

Convergence theorem does not address the issue of when to stop the iteration. It declares the approximate solution is good enough without stopping the iteration. Diving a stopping criterion is a better solution to address this issue. Even the error is small there is no direct way to know it.

• ║Xk-1 - Xk ║/║Xk║ if it is small enough then we stop.
• Check whether the residual║ f(Xk)║ is suitably to verify whether the problem is solved.
• Note both should not be simultaneously small.