I have two functions $f(x,y)$ and $g(x,y)$ for which I want to solve for the roots $(x^{*},y^{*})$ s.t. $f(x^{*},y^{*})=0$ and $g(x^{*},y^{*})=0$. The functions are transcendental -- being the sum of several exponentials -- but I know these roots do exist. I have tried to use a gradient method, but because the functions are so complex, I am not getting adequate roots. I know with optimization there is the possibility of using pattern search if gradient methods fail. What about roots? Is there any sort of method like pattern search that could solve for the roots of two transcendental equations?
Thank you.