Cholesky factorization

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Given an LaTeX: m \times m symmetric matrix LaTeX: A, a lower triangular matrix, LaTeX: L, is obtained, called the Cholesky factor, such that LaTeX: A = LL^T. This is particularly useful for solving linear systems, LaTeX: Ax=b, by using forward substitution, LaTeX: Ly=b, then backward substitution, LaTeX: L^T x = y. The original algorithm assumes LaTeX: A is positive definite, but it can apply more generally. This is also called Cholesky decomposition.


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