Hi, in the lack of a Numerical Analysis sub forum, I will post this question here as it is quite "calculus-ish".
Does there exist a error-bound on Regula Falsi (Method of False Position) similar to the one that the Bisection method has? I would like to have an expression for the number of iterations necessary as a function of some prespecified error.
Thanks.
Say that we have a function and we know that a root exists on .
If we use the method of false position, our first approximation to this root will be,
The next one is,
and so on..
What if I use a similar bound to the one in the bisection method, and say that
such that
where ?
Which depends of the function in question, unlike the bounds for bisection.
It would be interesting to see the error at the n-th step say in terms of bounds on the derivatives etc
(I don't think this impossible, just not worth the candle given false-positions other limitations and the nice properties of bisection - which does have its own problems when you have a double root)
CB