# Langevin curve fitting

1. Jun 24, 2008

### mhill

hi, there my question is let's suppose we have the magnetization (M) versus the applied field (H) as

$$M(H,T)= \sum _{n=1}^{N} W(x_i ) (x_i ) Lang (H.A.x_{i}/T)$$

here 'A' is a constant 'T' is the temperature of system Lang(x) is the Langevin function coth(x)-1/x ,

My problem is how to use a curve fitting algorithm to solve the problem ,i am working under the assumption that $$W(x_i)$$ i=1,2,3,....,N is a log normal distribution depending only on the value x_i

my curve fitting program is just 'Origin 7' i need the algorithm to curve-fitting to a certain given distribution W(x) thanks.

2. Jun 24, 2008

### per.sundqvist

What data do you have? Next, what does $$W(x_i ) (x_i )$$ mean? Could you give it analytical? Do you want to find A, and have a set of data like M_i=M(H_i,T_i) where _i is an index of your data points? Is x_i a random number or what?

I know how to find A for a problem of the type M_i=M(H_i,T_i) within matlab but that maby not help you, but the idea is based on non-linear least square minimization.

3. Oct 29, 2008

### mhill

thank you, if possible where could i learn 'Nonlinear least squares optimization' ??

4. Oct 29, 2008

### Dr Transport

Levenberg-Marquardt method....... try looking for that.