Tagging - 2020-04-01

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quid

1:34 AM

@MartinSleziak thanks that's great.

6 hours later…

Martin Sleziak

7:08 AM

new-tag A new tag cholesky-decomposition was created by Rodrigo de Azevedo and added to 16 questions. The same user created a tag-excerpt.

Cholesky decomposition

In linear algebra, the Cholesky decomposition or Cholesky factorization (pronounced /ʃo-LESS-key/) is a decomposition of a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte Carlo simulations. It was discovered by André-Louis Cholesky for real matrices. When it is applicable, the Cholesky decomposition is roughly twice as efficient as the LU decomposition for solving systems of linear equations. == Statement == The Cholesky decomposition of a Hermitian positive-definite matrix...

Q: Cholesky decomposition for special structure matrix

Suppose the matrix is of the form $\tilde{A} = aI -A^TA$, where $I$ is the identity matrix and $a>eig(A^TA)$. Assume that Cholesky decomposition is possible. Do we get a nice analytic expression or low cost computation for Cholesky decomposition of $\tilde{A}$?

Q: Cholesky decomposition of $A+kI$ given Cholesky decomposition of A

Suppose I have the Cholesky decomposition for a symmetric matrix $A$: $$ A = L L^T $$ I wish to compute the Cholesky decomposition for $A+kI$ where $I$ is the identity and $k$ is a scalar. Is there a way to obtain this using the decomposition for $A$ faster than recomputing the Cholesky decompo...

linear-algebra matrices matrix-decomposition cholesky-decomposition

Q: Cholesky of matrix plus identity

I have a positive definite matrix $A$ ($n \times n$ dimension) for which I have the Cholesky decomposition $A=LL^{'}$. I want to use this to compute a) The Cholesky decomposition of $A+c^2\times I $ where $c$ is a constant and $I$ is the identity matrix b) The Cholesky decomposition of $A+BB^{...

matrices computational-complexity matrix-decomposition cholesky-decomposition

Q: Relation between Cholesky and SVD

When we have a symmetric matrix $A = LL^*$, we can obtain L using Cholesky decomposition of $A$ ($L^*$ is $L$ transposed). Can anyone tell me how we can get this same $L$ using SVD or Eigen decomposition? Thank you.

matrices eigenvalues-eigenvectors matrix-decomposition svd cholesky-decomposition

Q: How to prove the existence and uniqueness of Cholesky decomposition?

Given a real Hermitian positive-definite matrix $A$ is a decomposition of the form $A=L L^T$ where L is a lower triangular matrix with positive diagonal entries. I read some proofs about the existence of Cholesky decomposition. Most of them start from LDU decomposition. Then the proof shows that ...