Incomplete Cholesky factorization
- Incomplete Cholesky factorization
In numerical analysis, a field within mathematics, 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".
References
*. See Section 10.3.2.
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