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Re: Beware of NSolve - nastier example
*To*: mathgroup at smc.vnet.net
*Subject*: [mg50346] Re: Beware of NSolve - nastier example
*From*: carlos at colorado.edu (Carlos Felippa)
*Date*: Sat, 28 Aug 2004 04:37:58 -0400 (EDT)
*References*: <200408200858.EAA12533@smc.vnet.net> <cg6srb$odf$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
Daniel Lichtblau <danl at wolfram.com> wrote in message news:<cg6srb$odf$1 at smc.vnet.net>...
< ... >
>
> On the flip side, the heuristics that decide when a root actually
> satisfies the equation can be a bit lax. Hence parasites can wind up in
> the returned solution set. One way to influence this is to rescale the
> equation e.g. multiplying by some large number.
>
> I'll look into tightening some of the decisions as to what constitutes a
> sufficiently small residual. The near-double-root issue goes with the
> territory and is in no way incorrect behavior.
>
> What is NR, by the way?
>
>
> Daniel Lichtblau
> Wolfram Research
Newton and Raphson from Olde England. Joseph Raphson was
rumored to be Newton's programmer.
BTW your suggestion to scale the equation does yield some
improvements -- at least no wrong roots appear:
f=10^8*(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]]]; (* gives 3 roots *)
Print[NSolve[f,x,16]]; (* 3 correct roots *)
Print[NSolve[f,x,21]]; (* 2 roots, missed 1 *)
Print[NSolve[f,x,24]]; (* 2 roots, missed 1 *)
Print[NSolve[f,x,28]]; (* 2 roots, missed 1 *)
Print[NSolve[f,x,32]]; (* 2 roots, missed 1 *)
Print[NSolve[f,x,64]]; (* 2 roots, missed 1 *)
Print[NSolve[f,x,128]]; (* 3 correct roots *)
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