Get coefficients of a closest logarithmic function to a set of data points I have a big set of points (x,y) which I want to interpolate by a function $$y=a\log(bx+c)+d$$
What is the best way to find a,b,c and d?
I tried Levenberg–Marquardt algorithm to iteratively find those coefficients, it works, but it seems like overkill. If there is something better and faster, please suggest it.

Assuming that you want to perform a curve fit.
You have $n$ data points$(x_i,y_i)$ and you want to use the model
$$y=a\log(bx+c)+d$$ First rewrite it as
$$y=a \log(1+\alpha x) + \beta \qquad \quad \text{where}\quad \alpha=\frac b c \quad \text{and}\quad \beta=a \log(c)+d$$
This model is nonlinear only because of $\alpha$. If you give $\alpha$ an arbitray value,
$$z_i=\log(1+\alpha x_i) \implies y=a z+\beta$$ and you immediately obtain $a$ and $\beta$ solving for these the normal equations
$$\sum_{i=1}^n y_i z_i= a\sum_{i=1}^n  z_i^2+\beta \sum_{i=1}^n  z_i$$
$$\sum_{i=1}^n y_i = a\sum_{i=1}^n  z_i +\beta \,n$$ and then
$$\text{SSQ}(\alpha)=\sum_{i=1}^n \big[a\,z_i+\beta-y_i \big]^2$$
Do it for a few values of $\alpha$ until you see more or less a minimum of $\text{SSQ}(\alpha)$ . At this point, you have consistent guesses and you can safely start a nonlinear regression or (why not ?) use Newton-Raphson method or Excel solver.
This should not take more than a couple of minutes.
