What Secrets the Bisection Method Hides?

[Namir]

Thanks ttw. Twenty years ago I was able to design a version of the Bisection algorithms to solve for the roots of a system of two nonlinear equation (F(x,y)=0 and G(x,y)=0. The difficulty in any such algorithm is to select the initial root-bracketing intervals (Ax,Ay) and (Bx, By) where the functions F and G have opposite signs. You can find that algorithm on my web site.

Perhaps I need to design another algorithm that helps find the proper interval for the above version of the Bisection method.

Namir