Fixed point iteration?

Question

One way to compute the value of π is to use fixed-point iteration. define g(x)=sin(x) + x. then finding the solution to g(x)=x is equivalent to solving f(x)=sin(x) =0. the fixed point iteration in this case can be written as: x(i+1)= g(x1)=sin(x1) + x1.

a) using the slope of g(x) near x=π, determine whether the fixed-point algorithm should converge or diverge.

b)perform the fixed-point iteration algorithms using a starting value of x=1. why does it converge so quickly?

Answer 1

I am not sure what your problem is. You seem to have an advanced course in maths. Convergence of iterative algorithms is a standard topic in text books. You should read them for better understanding.