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Traditionally, and in most of the "world" (literature), the convention that the Cholesky factor is lower triangular is the most common, i.e., $LL^T$. In MATLAB and Octave, among others (R's chol), Ch …

The missing entries are not uniquely determined, unless additional information is known. The only requirements on the missing entries are that they be symmetric, i.e., A(2,3) = A(3,2), A(2,4) = A(4,2 …

There's nothing wrong with the Cholesky factorization. There is an error in your code. See edit below. Here is MATLAB code and results, first for n_obs = 10000 as you have, then for n_obs = 1e8. For …

You need to take the transpose of the output of the MATLAB chol function. MATLAB defines Cholesky factor as upper triangular, and most of the rest of the world defines it as lower triangular. As used …

Solution Method A: If C is not symmetric, then symmetrize it. D <-- $0.5(C + C^T)$ Add a multiple of the Identity matrix to the symmetrized C sufficient to make it positive definite with whatever ma …