We investigate the application of the LR Cholesky algorithm to symmetric hierarchical matrices. The data-sparsity of these matrices make the otherwise expensive LR Cholesky algorithm applicable, as long as the data-sparsity is preserved. We will see that the data-sparsity of hierarchical matrices is not well preserved.
We will explain this behavior by applying a theorem on the structure preservation of diagonal plus semiseparable matrices under LR Cholesky transformations.