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non linear minimization

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gianluca
gianluca 2012-3-9
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

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回答（1 个）

Andrew Newell
Andrew Newell 2012-3-9
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.

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