Incomplete Cholesky factorization
In numerical analysis, an incomplete Cholesky factorization of a symmetric positive definite matrix is a sparse approximation of the Cholesky factorization. Incomplete Cholesky factorization are often used as a preconditioner for algorithms like the conjugate gradient method.
The Cholesky factorization of a positive definite matrix A is A = LL* where L is a lower triangular matrix. An incomplete Cholesky factorization is given by a sparse lower triangular matrix K that is in some sense close to L. The corresponding preconditioner is KK*.
One popular way to find such a matrix K is to use the algorithm for finding the exact Cholesky decomposition, except that any entry is set to zero if the corresponding entry in A is also zero. This gives an incomplete Cholesky factorization which is as sparse as the matrix A.
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- Incomplete Cholesky factorization] at CFD Online wiki
- Golub, Gene H.; Van Loan, Charles F. (1996), Matrix Computations (3rd ed.), Johns Hopkins, ISBN 978-0-8018-5414-9. See Section 10.3.2.
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