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I think the psuedocode is for a full Cholesky factorization.
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)
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content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
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I think the psuedocode is for a full Cholesky factorization.
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)