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Re: Beware of NSolve - nastier example

• To: mathgroup at smc.vnet.net
• Subject: [mg50218] Re: [mg50207] Beware of NSolve - nastier example
• From: DrBob <drbob at bigfoot.com>
• Date: Sat, 21 Aug 2004 03:04:19 -0400 (EDT)
• References: <200408200858.EAA12533@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

I hate to picture you typing in all those unnecessary Print statements, when this does exactly the same thing:

f = 5/432 - 11/(27*Sqrt[70]*Sqrt[19 - 1890*x]) + x/(2*Sqrt[38/35 - (108 + 1/10000000)*x]);

N[Solve[f == 0, x]](*OK, 3 roots #2, 4, 5 of a sextic poly*)
NSolve[f, x, 16](*6 roots, 3 wrong*)
NSolve[f, x, 21](*4 roots, 2 correct, 1 double wrong, 1 single wrong*)
NSolve[f, x, 24](*3 roots, 1 wrong*)
NSolve[f, x, 28](*3 roots, 1 wrong*)
NSolve[f, x, 32](*2 correct roots, missed 1*)
NSolve[f, x, 64](*2 correct roots, missed 1*)
NSolve[f, x, 128](*3 correct roots*)

Anyway, I think you just proved that Solve works better than NSolve for that problem.

Congratulations!

Bobby

On Fri, 20 Aug 2004 04:58:03 -0400 (EDT), Carlos Felippa <carlos at colorado.edu> wrote:

> This is a nasty one:
>
> f=5/432-11/(27*Sqrt[70]*Sqrt[19-1890*x])+x/(2*Sqrt[38/35-(108+1/10000000)*x]);
>
> Print[N[Solve[f==0,x]]]; (* OK, 3 roots #2,4,5 of a sextic poly *)
> Print[NSolve[f,x,16]];   (* 6 roots, 3 wrong *)
> Print[NSolve[f,x,21]];   (* 4 roots, 2 correct, 1 double wrong,
>         1 single wrong *)
> Print[NSolve[f,x,24]];   (* 3 roots, 1 wrong *)
> Print[NSolve[f,x,28]];   (* 3 roots, 1 wrong *)
> Print[NSolve[f,x,32]];   (* 2 correct roots, missed 1 *)
> Print[NSolve[f,x,64]];   (* 2 correct roots, missed 1 *)
> Print[NSolve[f,x,128]];  (* 3 correct roots  *)
>
> All 3 roots are single and well conditioned, no problem getting them
> in single precision with NR.
>
> Note: please reply to this newsgroup; DONT send mail to me directly
> (there is a white list, if not in list  your msg >null)
>
>
>



-- 
DrBob at bigfoot.com
www.eclecticdreams.net

• References:
  • Beware of NSolve - nastier example
    • From: carlos@colorado.edu (Carlos Felippa)