[SciPy-User] fsolve with restriction on variable

Warren Weckesser warren.weckesser@enthought....
Mon Aug 3 21:13:38 CDT 2009


Sebastian Walter wrote:
> well, I agree that is not such a clever idea to solve nonlinear
> systems by reformulating it as a NLP.
> But if the function F(x) =0 is uniquely solvable and f is twice
> continuously differentiable, then
> f(x) := |F(x)|^2 is also C^2 and should have a strict local minimum.
>   

Yes.
> Then Newton's method should locally converge quadratically.
>   

No,  because the derivative of the function being minimized is zero at 
the root.  In this case the convergence of Newton's method is only linear.


Warren

>
> On Mon, Aug 3, 2009 at 7:55 PM, Warren
> Weckesser<warren.weckesser@enthought.com> wrote:
>   
>> Harald Schilly wrote:
>>     
>>> On Mon, Aug 3, 2009 at 19:24, Ashley DaSilva<amd405@psu.edu> wrote:
>>>
>>>       
>>>> t I don't
>>>> want to find the minimum/maximum of my function, I want to find the root.
>>>>
>>>>         
>>> Very generally speaking, you can always find the root by minimization,
>>> if you square your function (simply because no negative values are
>>> possible)!
>>>
>>> H
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>>>       
>> But this is generally a poor method for finding a root.  It kills the
>> quadratic convergence of Newton's method, which is at the heart (in some
>> form or another) of most good root-finding algorithms.
>>
>> Warren
>>
>>
>> --
>> Warren Weckesser
>> Enthought, Inc.
>> 515 Congress Avenue, Suite 2100
>> Austin, TX  78701
>> 512-536-1057
>>
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