# Questions tagged [cholesky]

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11 questions
2k views

### Generate normally distributed random numbers with non positive-definite covariance matrix

I estimated the sample covariance matrix $C$ of a sample and get a symmetric matrix. With $C$, I would like to create $n$-variate normal distributed r.n. but therefore I need the Cholesky ...
5k views

### Can I use the Cholesky-method for generating correlated random variables with given mean?

I want to generate correlated random variables with a given correlation matrix, means, and variances. Does the Cholesky decomposition only work when the initial random variables are iids with the same ...
820 views

### How to do SVD instead of Cholesky for $L^{T}L$?

The Cholesky decomposition can be used to obtain $A$ from $X = AA^{T}$ (lower triangular version) but also $B$ from $Y = B^{T}B$ (upper triangular version). The SVD can be used to do something similar ...
309 views

### Explain how eigen helps inverting a matrix

My question relates to a computation technique exploited in geoR:::.negloglik.GRF or geoR:::solve.geoR. In a linear mixed model ...
596 views

### Mahalanobis distance with LDL decomposition

I've got an extended Kalman filter with innovation covariance defined as $\mathbf{W}=\mathbf{H}\mathbf{P}\mathbf{H}^\textrm{T} + \mathbf{R}$. I want to know the squared Mahalanobis distance $\|z\|^2$ ...
2k views

### Why use upper triangular Cholesky?

Software packages seem to prefer to work with the upper triangular part of the Cholesky factorization, see for example cholupdate. Why is this? It seems that it is ...
304 views

### Why is computing ridge regression with a Cholesky decomposition much quicker than using SVD?

By my understanding, for a matrix with n samples and p features: Ridge regression using Cholesky decomposition takes O(p^3) time Ridge regression using SVD takes O(p^3) time Computing SVD when only ...
332 views

### Generate random variables with predefined correlation structure AND fixing some values

I need to generate 4 random variables that show a predefined correlation structure Sigma AND where certain values of Vars 1-4 are fixed. As an illustrative example, consider the variables: ...
484 views

### Derivative of $x^T A^Ty$ with respect to $\Sigma$ where $A$ is (an upper triangle matrix and ) Cholesky decomposition of $\Sigma$

I would like to evaluate: $$\frac{ \partial x^T A^Ty}{\partial \Sigma}$$ where $A$ is a Cholesky decomposition of $\Sigma$ and an upper triangle matrix such that $\Sigma = A^T A$, $x$ and $y$ are a ...