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Re: [mg5070] [Q] FindRoot & large system of eqns
Posted:
Oct 30, 1996 12:19 AM


In my previous response to the post about FindRoot, I left out a modifier ("typically") that makes for an inaccurate statement. That last paragraph should have read:
> FindRoot is typically used for searching for a numerical solution to a single > equation. It uses a variant of Newton's method and hence requires some > initial guesses to get it started. It will use a secant method > if you provide two initial guesses.
The reason that I suggested other methods is that there is great difficulty finding solutions for large systems with Newton's method if you don't really know where to start; that is, if you cannot start with decent initial guesses. If you are just taking wild guesses for the initial values for such a system (16 unknowns in your case), you will almost certainly fail.
This is what you might see:
In[12]:= FindRoot[{x^23y==z, 2y^23xz^2==1, x+yz^2==3}, {x,1.0}, {y,2.0}, {z,4.0}]
FindRoot::"cvnwt": "Newton's method failed to converge to the prescribed accuracy after 15 iterations."
Out[12]= {x > 0.32227,y > 0.686455,z > 2.14173}
If, on the other hand, you are able to do some analysis and come up with good starting values, then FindRoot should server you quite well.
Paul Wellin



