LU Decomposition for solving linear equations in C++

Posted By: Achchuthan Yogarajah - 9:41 AM
Let A be a square matrix. An LU factorization refers to the factorization of A, with proper row and/or column orderings or permutations, into two factors, a lower triangular matrix L and an upper triangular matrix U,
 A = LU, \,
In the lower triangular matrix all elements above the diagonal are zero, in the upper triangular matrix, all the elements below the diagonal are zero. For example, for a 3-by-3 matrix A, its LU decomposition looks like this:

        \begin{bmatrix}
           a_{11} & a_{12} & a_{13} \\
           a_{21} & a_{22} & a_{23} \\
           a_{31} & a_{32} & a_{33} \\
        \end{bmatrix} =
      \begin{bmatrix}
           l_{11} & 0 & 0 \\
           l_{21} & l_{22} & 0 \\
           l_{31} & l_{32} & l_{33} \\
        \end{bmatrix}
        \begin{bmatrix}
           u_{11} & u_{12} & u_{13} \\
           0 & u_{22} & u_{23} \\
           0 & 0 & u_{33} \\
        \end{bmatrix}.

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