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Re: Bug in NSolve?


Andrzej Kozlowski <andrzej at tuins.ac.jp> wrote:

> Unlike Solve, NSolve  returns only one root when it finds multiple roots 
> it considers to be sufficiently close to be identical. In fact it seems 
> that it applies Union to the final result. So when you use more 
> precision the roots which were considered as distinct due to possible 
> error become identified and appear only once.
<snipped>
> Why do Solve and NSolve behave differently here? Well, it seems to me 
> that it is probably a matter of "philosophy". Solve is basically an 
> "algebraic function" and from the algebraic point of view the 
> multiplicity of roots is an important property of a solution. But most 
> people looking for numerical solutions would be I think inclined to 
> consider multiple roots as "the same".

But there should be two solutions, right? Solve returns:

In[1]:= Solve[4877361379 x^2 -9754525226 x + 4877163849==0,x]

               4877262613 - I Sqrt[2]         4877262613 + I Sqrt[2]
Out[1]= {{x -> ----------------------}, {x -> ----------------------}}
                     4877361379                     4877361379

The two solutions *are* close, as you wrote.

--
Bhuvanesh,
Wolfram Research.


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