A possible simple iteration rearrangement of the equation f (x) = 0 is in the form x = g(x) where g(x) = x − k(f(x)/f'(x)) and k is some real number.
Determine the values of the parameter k for which this simple iteration rearrangement is convergent, when finding the root of x^5 − 3x + 1 = 0 near x = 1.2.
Suggest a value of k that, in theory, should give the fastest rate of convergence.
What do I do here? Is this linear or quadratic convergence? Do I use this formula: |a-x_(n+1)|<= k|a-x_n|^p