Re: Bug in NSolve?

• To: mathgroup at smc.vnet.net
• Subject: [mg33855] Re: Bug in NSolve?
• From: lalu_bhatt at yahoo.com (Bhuvanesh)
• Date: Sat, 20 Apr 2002 02:49:43 -0400 (EDT)
• References: <a9oe60\$d9r\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```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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