How can I perform the modified Cholesky factorization/Decomposition in Mathematica?

Asked Dec 09 '18 at 10:25

Active Jun 10 '19 at 17:01

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How to "Modified" Cholesky Decomposition in Mathematica?

what I mean:

V = L . D . Transpose[L]

V is p*p(row is p,columns is p) non-negative definite matrix,
D is diag[$d\small1$,$d\small2$,$d\small3$,$d\small4$...$d\small p$] (Diagonal Matrix),
L is Lower triangular matrix,whose diagonal component is 1.

I found matlab package for example

OK,I've found that LDL factorization is called Modified Cholesky Decomposition. $\mathbf L\mathbf D\mathbf L^\top$ Cholesky decomposition

built-in (but undocumented) function?
Optimization`ModifiedCholeskyDecomposition

edited Jun 10 '19 at 17:01

asked Dec 09 '18 at 10:25

Xminer

What does "Modified" Cholesky Decomposition mean? Do you happen to mean $LDL^T$-factorization? – Henrik Schumacher Dec 09 '18 at 10:28
What code have you tried so far? Given an example input, what do you expect to get out? Please try to provide more details in the future. – MassDefect Dec 09 '18 at 10:32
yes,it seems LDL$T$ factorization(I was confused). thanks! – Xminer Dec 09 '18 at 10:46
As far as I know, Mathematica does not provide any built-in $LDL^T$-factorization. The factorizations provided by LinearSolve are $LU$-factorizations. – Henrik Schumacher Dec 09 '18 at 12:15

How can I perform the modified Cholesky factorization/Decomposition in Mathematica?

0 Answers0