I have a system of linear equations in form of $AX=b$ where $A_{m\times n}$, $X_{n\times 1}$ and $b_{m\times 1}$. Coefficient matrix $A$ is quite sparse. However, using a practical LP solver like LINGO it is clear that after permutation of rows, it turns out to be like a lower triangular matrix. I do not know what the permutation function should be. Since the matrix dimension is not square, I cannot use the LU decomposition to solve the system efficiently. Can you please let me know an efficient method for linear systems with nonsquare coefficient matrix?
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