[SciPy-User] fsolve with restriction on variable
Sebastian Walter
sebastian.walter at gmail.com
Mon Aug 3 17:23:21 EDT 2009
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.
Then Newton's method should locally converge quadratically.
Am I missing something here?
On Mon, Aug 3, 2009 at 7:55 PM, Warren
Weckesser<warren.weckesser at enthought.com> wrote:
> Harald Schilly wrote:
>> On Mon, Aug 3, 2009 at 19:24, Ashley DaSilva<amd405 at 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.
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