Nightmare Matrices: When Sparse Solvers Fail on GPUs

I introduce a family of difficult sparse matrices (“Nightmare matrices”) \(A\) designed to frustrate several common sparse direct and iterative strategies for solving \(Ax = b\). The construction is symmetric positive semidefinite, and is positive definite when the underlying random factor has full column rank, as it did here. I then analyze the performance of Krylov methods for these matrices on…