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Incomplete Cholesky Factorization

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Cholesky Factorization

When the square matrix A is symmetric and positive definite then it has an efficient triangular decomposition. Symmetric means that aij = aji for i,j = 1, ... , N. While positive definite means that

 v \bullet A \bullet v > 0   \forall v

In cholesky factorization we construct a lower triangular matrix L whose transpose LT can itself serve as upper triangular part.
In other words we have
L \bulletLT = A

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