Is there a way to compute the LDL^T factorization of a full matrix?? It seems that currently ldlt and LDLt support only SymTridiagonal and SparseMatrixCSC. However, lu works for full matrices. For example, using LinearAlgebra A = rand(4,4) B = Symmetric(A,:U) F = lu(B) F = ldlt(B) gives …

I definitely didn’t have a clear idea of what you were trying to do. Knowing that you are modifying a Hessian helps. If I’ve got it right now, it sounds like you’ve tried modifying the Hessian by flipping signs of negative eigenvalues, which left you with ill-conditioned matrices and are now aimin…

Thank you for your help and sorry for my late reply (I was out this weekend). Numerical stability is important in this case, so I need methods that consider matrix permutations. I think the best workaround for the moment is bunchKaufmann + ldl or directly ldlt(sparse(B)).

Is there anything which matches MATLAB’s ldl() ? How does MATLAB get around the numerical issues and gets L and D for any matrix?

https://fossies.org/linux/SuiteSparse/LDL/Doc/ldl_userguide.pdf looks interesting

I think the solution might be some synthetic sugar around the pivoted Cholesky decomposition so one gets out a structure which is similar to the non pivoted Cholesky.

If your matrix B is symmetric is the SVD decomposition not what you want ? B=USU’

No, because your matrix U must be lower triangular, not orthogonal.

[image] Shouldn't `bunchkaufman` be actually named `ldlt`? Numerics I am just musing over the choise of the name bunchkaufman for the bunkaufman function. If I understand it correctly, the function provides an implementation of an algorithm for LDLᵀ factorization of a symm…

[image] JM_Beckers: If your matrix B is symmetric is the SVD decomposition not what you want ? B=USU’ Pay attention that doesn’t hold for zero eigen values (Namely in that case it is not necessary that U = V ). Though you can always drop the zero singular values and then for the non zero su…

I’m late to this, but there are some things I’m not sure I understand about what you are trying to do. Given a symmetric matrix H, the goal sounds like it is to get a matrix absolute value \overline{H} (i.e. \overline{H} = (H^T H)^{1/2}, also known as the symmetric polar factor of H) so that you ca…

Thanks @mstewart for your detailed answer, and sorry for the late reply. I need to modify the Hessian in a Newton optimization algorithm. I need the modified Hessian to be positive definite to guarantee that the search direction is descendent. The first option was \overline{H}=V|\Lambda|V^T, but i…

LDLt factorization for full matrices

Specific Domains Numerics

zdenek_hurak May 16, 2022, 10:48pm 16

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LDLt factorization for full matrices

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