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MathGroup Archive 2002

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help in Numerical Intergation

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36518] help in Numerical Intergation
  • From: "Salman Durrani" <dsalman at itee.uq.edu.au>
  • Date: Tue, 10 Sep 2002 06:24:52 -0400 (EDT)
  • Organization: The University of Queensland, Australia
  • Sender: owner-wri-mathgroup at wolfram.com

Hi

I am having some trouble with numerical integration.

\!\(\(\(Timing[
    ansOUT = {}; \[IndentingNewLine]For[EbNo = 0, EbNo <= 2,
      EbNo += 10\/10, \[IndentingNewLine]linEbNo =
        10\^\(EbNo\/10\); \[IndentingNewLine]M = 64; \[IndentingNewLine]K =
        Log[2, M]; \[IndentingNewLine]p = \(M/2\)\/\(M - 1\)\ Sum[
            Binomial[M - 1,
                n] \((\(-1\))\)\^\(n + 1\)\/\(1 + n\)\ Exp[\(-\
                    linEbNo\)\ K\ n\/\(1 + n\)], {n, 1,
              M - 1}]; \[IndentingNewLine]Pm = \(1\/\@\(2\ \[Pi]\)\)
          NIntegrate[
            1 - \(\((\(1\/\@\(2\ \[Pi]\)\)
                        NIntegrate[
                          Exp[\(-x\^2\)\/2], {x, \(-\[Infinity]\), y},
                          WorkingPrecision -> 32\ ])\)\^\(M - 1\)\)
                Exp[\(\(-1\)\/2\) \((y - \@\(2\ K\ linEbNo\))\)\^2], {y,
\(-\
\[Infinity]\), \[Infinity]},
            WorkingPrecision ->
              32]; \[IndentingNewLine]Pb = \(\(M/2\)\/\(M - 1\)\)
          Pm; \[IndentingNewLine]AppendTo[
        ansOUT, {N[a, 4], N[p, 8],
          N[Pb, 8]}];\[IndentingNewLine]];]\)\(\[IndentingNewLine]\)\)\)
TableForm[ansOUT]

The code can also be downloaded from
http://www.itee.uq.edu.au/~dsalman/_downloads/Proakis.nb

Col. 2(symblic formula) and 3 (result of numerical integration) of the
variable ansOUT should be identical.

However the numerical integration is giving a 0 answer.

Can anyone please suggest how a solution to this problem.

Thanks

Salman











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