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Using Solve[] for Advanced Systems?

William Duhe
Posted 8 years ago

I am having some trouble understanding the limitations and of Solve[]. Bellow I have a function that I am trying to use to solve for some of the parameters inside.

I get the error:

Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help.
POSTED BY: William Duhe
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Two problems. One is that Solve has no idea what the function is since it is undefined for symbolic input. So use FindRoot since that can handle a function defined as a black box, that is, only giving a result for explicit numeric input. Next problem is that PutTK is only defined for nine inputs, but four of the five calls have ten inputs.
POSTED BY: Daniel Lichtblau
William Duhe
William Duhe
Posted 8 years ago

Just edited the post, I had copied the test in incorrectly - thanks for catching that. I will look into using FindRoot- what if I don't know the initial points to start scanning from though?

FindRoot[{PutTK[95,0.001,\[Sigma],1,\[Gamma],a,b,0.001,.1]==6.45,PutTK[100,0.001,\[Sigma],1,\[Gamma],a,b,0.001,.1]==8.35,PutTK[90,0.001,   \[Sigma],1,\[Gamma],a,b,0.001,.1]==4.93,PutTK[85,0.001,\[Sigma],1,\[Gamma],a,b,0.001,.1]==3.73,PutTK[80,0.001,\[Sigma],1,\[Gamma],a,b,0.001,.1]==2.80},{{\[Sigma],1},{\[Gamma],1},{\[Lambda],1},{a,1},{b,1}}]

FindRoot gives me the error:

"Encountered a singular Jacobian at the point {[Sigma],[Gamma],\ [Lambda],a,b} = {1.,1.,1.,1.,1.}. Try perturbing the initial point(s)"
POSTED BY: William Duhe

All the variables:

 ?, ?, ?, a, b

have some meaning right? I.e. should they be real? i.e. positive? integer? smaller than x? I tried a bit around but your function PutTK is very sensitive and can give values of 10^500 for some choices of the above variables. Perhaps specify that the variables should be within some limits can certainly help a lot in searching. Hard to tell without knowing where the model came from...
POSTED BY: Sander Huisman
William Duhe
William Duhe
Posted 8 years ago

Also, how is able to solve for a single variable and not multiple?
POSTED BY: William Duhe
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