Solving equations in C

Question

I need to solve the following equation in C:

a + ln(a) = x

I know the value of x and I need to find the value of 'a' that satisfies this equation. Can anyone suggest an efficient method for solving this equation. May be Newton Raphson, or anything more efficient ?

It's numerical methods, so SO should be fine. Anything wrong with using N-R? — kfmfe04, Oct 11 '12 at 05:45
I need something more efficient, since this is for a real time calculation. — Ashwin, Oct 11 '12 at 05:53

score 2 · Answer 1 · answered Oct 11 '12 at 05:55

Newton Raphson Method will do good but I suggest that you try out Lambert W function.
W(x) = inverse of the function f(x)= xex.
So, in your case ln(a)+ a= x, then, taking the exponential of each side, eln(a)+ a= aea= ex. This gives you a=W(ex).
Now, you can apply approximations to solve this. But first, I suggest that you read about Lambert method carefully.

Solving equations in C

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