Question

Suppose we modify the bisection method into the following variation: for each step, with bracketing interval [a,b], approximations are chosen at the location (2a + b)/3, but the interval is cut into two at the different location (a + 3b)/4.

(a) Calculate the first 2 approximations p1,p2 for this variation when f(x) = cosx−x with starting interval [0,π/2].

(b) Bound the absolute errors of the approximations pn for a starting interval of length L.

Answer 1