This function uses Ridder's Method to do non-linear root finding. This method works well for smooth scalar functions, and requires a bounded search space.
% XZERO = ROOTSOLVE(FUNC, XLOW, XUPP, TOL)
% FUNCTION: This function uses Ridder's Method to return a root, xZero,
% of func on the interval [xLow,xUpp]
% func = a function for a SISO function: y = f(x)
% xLow = the lower search bound
% xUpp = the upper search bound
% tol = return xZero if abs(func(xZero)) < tol
% xZero = the root of the function on the domain [xLow, xUpp]
% 1) The function must be smooth
% 2) sign(f(xLow)) ~= sign(f(xUpp))
% 3) This function will return a root if one exists, and the function is
% not crazy. If there are multiple roots, it will return the first one
% that it finds.
Great point. I do use fzero for the most root-finding applications. I wrote this function for two reasons:
1) I use Matlab Coder to compile much of my code to MEX. The fzero command is not compatible with Matlab Coder (at least at the time of writing), while this implementation is (with slight modifications).
2) This code was used as a test implementation (checking results against fzero) for a root-solving function that I wrote in Java for a contact solver in a physics engine.
This method is one of several used within the standard MATLAB function fzero. fzero changes methods based on the results of each iteration. Doing so make the function quite robust. So, I don't know what value this function has.
Added feature: the user can now specify the convergence tolerance.
Fixed a small bug: the tolerance for checking roots on the boundary of the interval was set to 0, rather than the convergence tolerance.