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4 votes
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Why R function Chol() breaks for Hilbert matrices of order n > 12

Both Zen's comment and F.Tusell's answer are correct (+1 to both). Just to add a bit on this: If you look at the associated eigenvalues of Hilbert(13) for a example, the smallest of them is smaller in …
usεr11852's user avatar
12 votes
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Why does the resulting matrix from Cholesky decomposition of a covariance matrix when multip...

As explained in my comment, the inconvenient truth is that the Cholesky decomposition while usually defined as $K=LL^T$ where $L$ is lower triangular, is equally valid as $K=U^TU$ where $U$ is upper t …
usεr11852's user avatar
4 votes
Accepted

Cholesky factorization and forward substitution less accurate than inversion?

For most cases Cholesky factorization should be a faster and more numerically stable method for solving a linear system of equation such as $Ax=b$ given that $A$ is describing a positive definite matr …
usεr11852's user avatar