Write a MATLAB function recursivebisection.m that takes as inputs an initial bra

Question

Write a MATLAB function recursivebisection.m that takes as inputs an initial bracketing [xl,xr and the desired tolerance TOL. and determines the solutions of the equation f(x) = 0 using the recursive bisection method discussed in Section 2.2 of the text. Find all three roots, to 6 significant figures, with TOL = 10^-8. To determine suitable brackets for finding multiple roots you will have to explore this function a bit using the MATLAB plot command. You can change how variables are displayed to the MATLAB Command Window by typing format long.

Explanation / Answer

Bisection works by taking endpoints of some initial interval [a,b] and finding which half of the interval must contain the root (it evaluates the midpoint, and identifies which half has the sign change). Then bisection repeats the process on the identified half.

Bisection converges upon only one possible root, and if your function has multiple roots inside [a,b], it is difficult to predict in general which specific root it will converge to. (Note: since bisection is a fully deterministic algorithm, it will always converge to the exact same root if you give it the same initial interval.) The iterations simply refine your approximation of found root, they do not find multiple roots.

exists. Then:

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