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However, beaware that by default, Simplicial LLT applies a symmetric permutation to reduce fill-in.

The Melenchon and Martinez paper outlines a relatively simple implementation if you are inclined to try your hand (in which case please publish it! Update on the matter: I looked around the Eigen library offers a rank update for their $LDL^T$ decomposition (ie.2000) and "Efficiently downdating, composing and splitting singular value decompositions preserving the mean information" (Melenchon and Martinez, 2007); I came across a paper that implements among other things decremental LDA - Incremental and decremental LDA learning with applications (Pang et al. I have not come across any decremental SVD routines.For a particular problem if there are at most one or two consecutive down-dates regarding the most recent points (eg.2008) are well-cited papers than can offer a good starting point.The whole idea is the "forgetting vector" to something very small will lead us to obtain essentially a new eigen-decomposition for $n 1$ points given we already have seen $n$ points.