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  "body": "\n## Summary\n\nAn incomplete Cholesky factorization of a sparse symmetric positive definite matrix $A$ is a sparse lower triangular matrix $L$ with $L L^T \\approx A$.\nIt is computed like the [[Cholesky decomposition|0WKG8CYY6A]], but every entry outside a prescribed sparsity pattern is dropped.\nIts main use is as a [[preconditioner|KE98SW3SBD]] for the conjugate gradient method.\n\n## Explanations\n\n### L1 human\n\nThe exact Cholesky factor of a sparse matrix is often much denser than the matrix itself.\nThe incomplete factor keeps only the entries in allowed positions, for example the positions where $A$ itself is nonzero.\nThe result is cheap to store and to use, and $L L^T$ is close to $A$, though not equal.\nSolving with $L L^T$ then serves as a fast rough inverse of $A$ inside an iterative method.\n",
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