       Re: Beware of NSolve

• To: mathgroup at smc.vnet.net
• Subject: [mg50169] Re: [mg50165] Beware of NSolve
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Wed, 18 Aug 2004 04:34:04 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```On 18 Aug 2004, at 07:20, Carlos Felippa wrote:

> Run v. 4.2 on Mac:
>
> f=5/432 - 11/(27*Sqrt*Sqrt[19 - 1890*x]) + x/(2*Sqrt[38/35 -
> 108*x]);
>
>  Solve[f==0,x]  returns 2 real roots:
>
> {{x -> (-171 - 25*Sqrt)/30240}, {x -> (-171 +
> 25*Sqrt)/30240}}
>
> NSolve[f==0,x]  returns 4 real roots:
>
> {{x -> -0.10481082961146104}, {x -> -0.014126116704662378},
>  {x -> 0.002816592895138556}, {x -> 0.0003796126802330315}}
>
> Roots 1 and 4 are incorrect.  (Just plot f)
>
> Had a similar problem with a quartic 3 months ago.  This is a
> simpler example.
>
>
>
In this case as in many others involving numerical compoutations it is
just the question of the working precision. This is just a "fact of
life" of numerical mathematics

f = 5/432 - 11/(27*Sqrt*Sqrt[19 - 1890*x]) +
x/(2*Sqrt[38/35 - 108*x]);

NSolve[f == 0, x]

Out=
{{x -> -0.1048108296114584},
{x -> -0.014126116704662336},
{x -> 0.0028165928951385585},
{x -> 0.0003796126802330329}}

but

NSolve[f == 0, x, WorkingPrecision -> 100]

{{x -> -0.01412611670466236638824490631656833001879549658\
023713039810018063813686176066910885658666635943993612512\
76942823094`99.69897000433602},
{x -> 0.00281659289513855686443538250704452049498597277\
071332087429065682861305223685958504706285683563041231560\
38847579695`99.69897000433602}}

Andrzej Kozlowski
Chiba, Japan
http://www.mimuw.edu.pl/~akoz/

```

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