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How to calculate the numerical integral of the type $ \int_a^b e^{x^2} dx $ efficiently?

My problem is:

we need to compute repeatly the integral:

$ \frac{\int_{|m|=1}mm \exp(B\mathbin:mm)\,dm}{\int_{|m|=1}\exp(B\mathbin:mm)\,dm}$ where

  1. $:$ means $A\mathbin:B=\sum_{i,j}A(i,j)*B(j,i)$
  2. m is a 1 dimensional tensor, $m \in R^{1\times 3}$
  3. B is a traceless diagonalizable two dimensional tensor.
  4. $mm$ means the tensor product $m \otimes m$
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    It's a tensor. It's proved it can be diagonalized by the same matrix as B.2012-03-24

0 Answers 0