# SuperLU vs Direct Substructuring

The eigenproblem solver in my master's thesis used SuperLU, a direct solver for the solution of systems of linear equations (SLE) $Ax = b$. For the largest test problems, the eigensolver ran out of memory when decomposing the matrix $A$ which is why I replaced SuperLU with direct substructuring in an attempt to reduce memory consumption. For this blog post, I measured set-up time, solve time, and memory consumption of SuperLU and direct substructuring with real symmetric positive definite real-world matrices for SLEs with a variable number of right-hand sides, I will highlight that SuperLU was deployed with a suboptimal parameter choice, and why the memory consumption of the decomposition of $A$ is the wrong objective function when you want to avoid running out of memory.