Following on from the topic here:
viewtopic.php?f=74&t=111513

There was a suggested and welcome improvement to the following code:

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// [1] Un-numbered equation after (5).
const Eigen::MatrixBase<Derived4> L = C_un_obs_p * C_obs_obs_p.inverse();


Namely,

ggael wrote:Moreover, you'll get faster and more accurate result without explicitly inverting the matrix, e.g.:

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L.transpose() = C_obs_obs_p.transpose().lu().solve(C_un_obs_p.transpose());


In the future, Eigen will do this rewriting for you. Currently avoid .inverse() unless you really want it!

Since C_obs_obs_p is a symmetric positive-defininte matrix, is there an improved method for this (e.g. LLT)?

yes, if it's symmetric positive definite then you can use .llt() instead of .lu()