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Results tagged with svd
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user 26323
Singular value decomposition (SVD) of a matrix $\mathbf{A}$ is given by $\mathbf{A} = \mathbf{USV}^\top$ where $\mathbf{U}$ and $\mathbf{V}$ are orthogonal matrices and $\mathbf{S}$ is a diagonal matrix.
22
votes
3
answers
10k
views
Cholesky versus eigendecomposition for drawing samples from a multivariate normal distribution
I would like to draw a sample $\mathbf{x} \sim N\left(\mathbf{0}, \mathbf{\Sigma} \right)$. Wikipedia suggests either using a Cholesky or Eigendecomposition, i.e.
$
\mathbf{\Sigma} = \mathbf{D}_1\mat …
- 695
14
votes
Accepted
Cholesky versus eigendecomposition for drawing samples from a multivariate normal distribution
Consider the SVD of a PSD matrix, $P = USV^T$. Since P is PSD, this is actually the same as the ED with $P = USU^T$. … The SVD is much more
numerically stable for nearly singular covariance matrices than the
ChD.
Reference:
Straka, O.; Dunik, J.; Simandl, M. & Havlik, J. …
- 695