LU decomposition

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A factorization of a matrix LaTeX: A into a lower triangular matrix LaTeX: (L) and an upper triangular matrix LaTeX: (U) so that LaTeX: A=LU. The advantage is to solve the system LaTeX: Ax=b, we first apply forward substitution to solve LaTeX: Ly=b, then backward substitution to solve LaTeX: Ux=y.


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