3 problems

Weak-sparsity-dependence conjecture. The error of the approximate Cholesky factorization depends weakly on the number of non-zeros in the input Laplacian matrix.

Let the Krylov matrix be formed from a random matrix with $\frac{}{}$ non-zeros per column as in the preceding minimum singular value bound, and consider both the sparse Krylov con…

Let an ILU(0) preconditioner be applied to a sparse linear system with coefficient matrix, and measure the approximation accuracy of its preconditioning matrix as in the paper. Coe…