non linear minimization

Hi, I've this function which describes the temperature T vs depth z

T(i) = T0 - (H(i).*z(i).^2)./k(i) + ((Q.*z(i))./k(i))

where H(i) and k(i) are known vectors (n x 1) of the same size of z(i) which describe the heat source and thermal conductivity vs depth, respectively. I know temperature measurements at some depth

   T = [0 18;1000 52; 1154 55]

I would solve this function for Q (surface terrestrial heat flow). Probably the commands lsqnonlin or fsolve could help me but I do not know how to do. Thanks for the help.

Gianluca

Answer 1

[Andrew Newell]

The simplest approach would be to invert the equation to get

Q = ((T-T0).*k +(H.*z.^2))./z;

This will give you three estimates of Q. Take the mean of them.