# Efficient calculation of the multivariate normal density function

The formula for the multivariate normal density function in the standard form contains $\Sigma^{-1}$ and the determinant of $\Sigma$, which are not very computationally friendly. Is it possible to calculate the density in some other way, that is more suitable for computer implementation?

EDIT: To be precise I am after the log of the density function, if it helps.

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 why do you say $\Sigma$ is not computer friendly? – mathemagician Jan 17 at 13:13 @mathemagician, calculating determinants and inverse matrices is not computer friendly in general, because they are slow and numerically unstable (that's what I have been told at least!) – Grzenio Jan 17 at 13:15 It is not that bad if you use good software packages. It could all go wrong tho if the matrix has both very large and very small numbers, as a process called floating point numbers is used. I don't know any further about this, but I use R and it works fine, even with very large matrices. – mathemagician Jan 17 at 13:25