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MathGroup Archive 2004

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Re: Simple question or how Mathematica getting on my nerves.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45862] Re: Simple question or how Mathematica getting on my nerves.
  • From: drbob at bigfoot.com (Bobby R. Treat)
  • Date: Tue, 27 Jan 2004 04:51:32 -0500 (EST)
  • References: <butdvt$9se$1@smc.vnet.net> <bv006g$jc9$1@smc.vnet.net> <bv2f57$2r$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Surely someone will come up with a better example, but here are
several computations of the identical (in theory) expression. Change
k, and you'll see various behaviors. The first element of the output
list is accurate to as many places as shown. The others are wrong to
varying degrees. I didn't use Sum, because it adds in a smart order; I
wanted to control things. (try setting addTable=Sum)

The really curious thing is that the third and fourth results should
be identical (I think) but they aren't! Also, using
Attributes[addTable] = {HoldAll} changes several answers.

add[x_List] := 
  (For[sum = 0; i = 1, 
    i <= Length[x], i++, 
    sum += x[[i]]]; N[sum])
Attributes[addTable] = {};
addTable[x__] := add[Table[x]]
first = 20; 
last = 40; 
k = 20; 
a = 20/9; 
InputForm[
  N[{addTable[a^(-n) - 
      (a + 10^(-k))^(-n), 
     {n, first, last}], 
    addTable[N[a^(-n)] - 
      N[(a + 10^(-k))^(-n)], 
     {n, first, last}], 
    add[Table[
      N[a^(n - first - 
          last)] - 
       N[(a + 10^(-k))^
         (n - first - last)], 
      {n, first, last}]], 
    addTable[
     N[a^(n - first - 
         last)] - 
      N[(a + 10^(-k))^
        (n - first - last)], 
     {n, first, last}], 
    addTable[N[a^(-n)], 
      {n, first, last}] - 
     addTable[N[(a + 10^(-k))^
        (-n)], {n, first, 
       last}], addTable[
     N[a^(-n)] - 
      N[(a + 10^(-k))^
        (n - first - last)], 
     {n, first, last}]}]]
{1.9748897304222703*^-26, 0., 
  9.137784495123884*^-24, 0., 
  0., 
  -1.3234889800848443*^-23}

Bobby

Harold.Noffke at wpafb.af.mil (Harold Noffke) wrote in message news:<bv2f57$2r$1 at smc.vnet.net>...
> Bob:
> 
> In your reply to George you wrote ...
> 
> > Although NIntegrate works without explicitly increasing the precision.  
> > So the precision is impacted by the sequencing of the calculations.
> >
> > NIntegrate[k[f], {f, 0.6214, 0.5242}]
> >
> > -0.139838
> 
> Can you explain what you meant by "sequencing of the calculations"?  I
> calculated the integral shown above after restarting Mathematica, and
> I obtained the answer shown above.
> 
> Regards,
> Harold


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