Solving a single non-linear equation given by a vector of values and having a lot of parametrs efficiently.

Dear All, I have the following problem: I have an equation f(x,a,b,c,d,e) = 0, where x is a variable and other letters represent parameters. The equation f is given by a vector of values and not by an analytic formula. These points form a monotonic, nonlinear shape that does not necessarily cross the zero line (then the equation has no solution).

I am solvig the equation by flipping the axes (i.e. rotating the graph of the function by 90degress to the left) and by interpolating the value of the function in zero: x = F(y,a,b,c,d,e), where F is the rotated function and y = 0. This method works well but it is inside of a multiple parallelized for loop. Unfortunately, it is still slow because of the curse of dimensionality. Matlab does not allow the interpolation routine to be vectorized so the loops are necessary.

Can anyone suggest a faster solution ?