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If A is a symmetric matrix, is there a fast algorithm for LU factorization? I know this algorithm for non-symmetric matrix.

    For k = 1,..,n        For i = k + 1,...,n          mult := a_{ik}/a_{kk}          a_{jk} := mult          For j = k+1,...,n              a_{ij} := a_{ij} - mult * a_{kj}          Endfor      Endfor    Endfor 
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    Look up the $\mathbf L\mathbf D\mathbf L^\top$ and Cholesky decompositions. Of course, these method will only work if all the leading submatrices of your symmetric matrix are nonsingular; otherwise, (symmetric) pivoting is necessary.2012-08-12
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    Use Lapack. $ $2012-11-26

2 Answers 2