Section: New Results

Constructing elimination trees for sparse unsymmetric matrices

The elimination tree model for sparse unsymmetric matrices and an algorithm for constructing it have been recently proposed [50] , [51] . The construction algorithm has a worst-case time complexity of $\Theta \left(mn\right)$ for an $n\times n$ unsymmetric matrix having $m$ off-diagonal nonzeros. We proposed [53] another algorithm that has a worst-case time complexity of $𝒪(mlogn)$. During this reporting period, we compared the two algorithms experimentally and showed that both algorithms are efficient in general. The known algorithm [51] is faster in many practical cases, yet there are instances in which there is a significant difference between the running time of the two algorithms in favor of the proposed one.