Talk:Incomplete Cholesky factorization
I think the psuedocode is for a full Cholesky factorization.
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Problem with pseudocode
I think the psuedocode is for a full Cholesky factorization.
^ That should be fixed as of Jan 4, 2026. Rileyjmurray (talk) 19:18, 5 January 2026 (UTC)
Non-existence of the ICF for non-diagonally-dominant matrices should be stated
The article misses to state that the incomplete Cholesky factorization does not necessarily exist even when the (symmetric positive definite) matrix has a full Cholesky factorization. This is a of practical relevance for problems where the matrix is not diagonally dominant, for example for linear systems arising from implicit differential equation solvers when the time step is large. It would also be useful to propose how a modified Cholesky preconditioner can be obtained in such cases. Pia novice (talk) 10:49, 18 December 2023 (UTC)
- I've added a statement about the possibility of non-existence. I didn't add anything about how to handle that case. The "Templates for linear systems" book has plenty of discussion on that topic which could be included in this article. That said, it'd be easy to exceed the scope of this article and end up discussing incomplete triangular factorizations more generally (e.g., incomplete LU, incomplete LDLT, even sparse incomplete QR). Rileyjmurray (talk) 19:20, 5 January 2026 (UTC)
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