Christopher James Huff wrote:
> 
> This is also close to the regula falsi or false secant method. The idea 
> with this method is that when you have a pair of points that bracket a 
> root, approximate the function as linear within that interval and use 
> the computed root as the new splitting point. It is similar to Newton's 
> method, but doesn't require a derivative of the function. It converges 
> faster than bisection in most cases, but is only guaranteed to converge 
> if you start out with a bracketed root. I've considered using a variant 
> of this as a second stage to the isosurface root solver...use bisection 
> to locate the roots to within a certain crude precision, and then use 
> regula falsi to refine the roots.

I am quite sure you will miss some intersections this way (cases where 
the function is negative only in a very small interval along the ray and 
is positive otherwise for example).

Christoph

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