solving a nonlinear equation faster

Dear all,

I want to solve this equation

 -0.5+ 0.5*a*exp(-x-b*c) -(x-d)/e=0

where a,b,c,d are known quantities that change in each iteration of the algorithm.

So, I use the following code

 x0=1;
  Myfun = @(x, a, b, c,d,e) -0.5+ 0.5*a*exp(-x-b*c) -(x-d)/e;
  A=fzero(@(x)Myfun(x, a, b, c,d,e),x0);

However, I noticed that this code is slow. So I tried something like

 ff=0;
   while abs(ff) > 0.0001  
      ff= -0.5+ 0.5*a*exp(-x-b*c) -(x-d)/e;
      g=-0.5*a*exp(-x-b*c) -1/e ;
      x = x - ff/g;
   end

where g is the first derivative of the main function ff.

But I do not get similar solutions. Do you thing that the second piece of code is wrong?

Answer 1

[Walter Roberson]

It has an exact solution:

lambertw((1/2)*a*e*exp(-b*c-d+(1/2)*e))+d-(1/2)*e

You will need the Symbolic Toolbox for lambertw

[ektor]

It is extremely slow in my code

[Walter Roberson]

On my system, with numeric a, b, c, d, e, it takes about 6E-5 seconds each, which is very reasonable.