Regula Falsi this has been bothering me for days

[relinquished™]

Hello again. I'm kinda stuck trying to prove that the Order of Convergence for the Method of False Position (Regula Falsi) Iteration for finding roots is somewhere between 1 and the golden ratio (approx. 1.62). I do know that

$$c_k = \frac{f(b_k)a_k - f(a_k)b_k}{f(b_k)-f(a_k)}$$

Which tells me that the error caused by using such a method could be bounded by the length of the interval [a,b]. Problem is that I don't know how to bound it since the numerator is obviously no a simple b-a like the bisection method. Also, the denominator for the iterative method constantly changes since either the values of a or b are changed for the next iteration. Any suggestions?

Thanks,

reli~

 

[island-boy]

hi
the order of convergence of the regular falsi method is 1, not between 1 and the golden ratio.

hint:
since both the values of a and b changes for the next iteration, use cases. There are only 2 when c = a or when c = b. Both will result to similar answers.